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Int Workshop on Nuclear Dynamics in HIR and Neutron Stars Beijing Normal University 9-14 July 2007
outline bull observational data of neutron starsbull microscopic hadron EoS from pure baryon to composite matter (leptonsYKmacr) bull onset of transition to quark phasebull confinement models of quarksbull M-R diagram of NS from general relativity (TOV)
EoS of Nuclear Matter and Structure of Neutron Stars
preliminary remarks
nuclear matter is an homogeneous system made of rigid nucleons interacting via the nuclear force (surface and coulomb effects are neglected)
neutron stars are compact astrophysical objects mostly born after the explosion ofsupernovae They are supposed to be made of nuclear matter in their interior
But the way they were born the neutron stars in the inner core are not simply made of nucleons but of neutrons and protons in equilibrium with leptons (electrons and muons)and we should assume that at increasing density the threshold for the production of new particles
is reached hyperons kaons and quarks
Therefore we will deal with asymmetric nuclear matter
beta-equilibrium with electrons and muons p + emacr n + hyperonized matter n + n n + ( p + macr) at gt 2o
kaon condensation n p + Kmacr at gt 2-3o
transition to quark matter HP QP (uds) at ~ 6o
view of a neutron star
Crust pinningthermalemissionhellip ( Cao talk)
Interior
NK Glendenning Compact Stars Nuclear Physics Particle Physics Springer 2000
Facts about Neutron Stars
bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gauss
Observed Masses three main families
PSR J0751+1807 M gt 21plusmn03 Mcopy
PSR 1913+16M = 144 Mcopy
J Lattimer
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
preliminary remarks
nuclear matter is an homogeneous system made of rigid nucleons interacting via the nuclear force (surface and coulomb effects are neglected)
neutron stars are compact astrophysical objects mostly born after the explosion ofsupernovae They are supposed to be made of nuclear matter in their interior
But the way they were born the neutron stars in the inner core are not simply made of nucleons but of neutrons and protons in equilibrium with leptons (electrons and muons)and we should assume that at increasing density the threshold for the production of new particles
is reached hyperons kaons and quarks
Therefore we will deal with asymmetric nuclear matter
beta-equilibrium with electrons and muons p + emacr n + hyperonized matter n + n n + ( p + macr) at gt 2o
kaon condensation n p + Kmacr at gt 2-3o
transition to quark matter HP QP (uds) at ~ 6o
view of a neutron star
Crust pinningthermalemissionhellip ( Cao talk)
Interior
NK Glendenning Compact Stars Nuclear Physics Particle Physics Springer 2000
Facts about Neutron Stars
bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gauss
Observed Masses three main families
PSR J0751+1807 M gt 21plusmn03 Mcopy
PSR 1913+16M = 144 Mcopy
J Lattimer
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
view of a neutron star
Crust pinningthermalemissionhellip ( Cao talk)
Interior
NK Glendenning Compact Stars Nuclear Physics Particle Physics Springer 2000
Facts about Neutron Stars
bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gauss
Observed Masses three main families
PSR J0751+1807 M gt 21plusmn03 Mcopy
PSR 1913+16M = 144 Mcopy
J Lattimer
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
NK Glendenning Compact Stars Nuclear Physics Particle Physics Springer 2000
Facts about Neutron Stars
bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gauss
Observed Masses three main families
PSR J0751+1807 M gt 21plusmn03 Mcopy
PSR 1913+16M = 144 Mcopy
J Lattimer
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Observed Masses three main families
PSR J0751+1807 M gt 21plusmn03 Mcopy
PSR 1913+16M = 144 Mcopy
J Lattimer
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Yakovlev et al
Non superfluid Superfluid
Thermal evolution
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
p + e- n + e
n p + e- + e
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
due to the poor information from NS we need to make theoretical predictionsas much accurate as possible
for the EoS of nuclear matter the state of art is quite reasonable since thetheory of nuclear matter has undergone a long term development reaching a highDegree of sophistication
The description yperon matter is also satisfactory since we know the N-Y force even we still donrsquot know the Y-Y force (see Dang and Takatsuka talks)
the interaction N-K is less known and all predictions for the k condensationare still model-dependent (see Sun talk)
for the quark phase we have many theories still waiting constraints (Gao LiuMaruyama Huang Di Torotalks)
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Hadron EoS
from the NN experimental phase shifts two-body realistic interactions
from B-W nuclear mass formulasaturation properties
EA = -16 MeV = 17 fm-3
KA = 220 MeV (monopole)Esym =30 MeV
--empirical constrains --
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
SP
Coester et al Phys Rev C1 769 (1970)
Saturation curve within the BBG ldquogap choicerdquo (U(k)=0 if kgekF) and Av14
BBG ldquocontinuous choicerdquo
Similar results within the Variational Method Possible corrections many-body forces andor relativistic effects
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Nucleon-Nucleon Interaction Argonne v18
(Wiringa Stoks amp Schiavilla Phys Rev C51 38 (1995))
Neutron Matter
Symmetric Matter
Dependence on the many-body scheme
APR Variational (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Catania group BHF (Akmal Pandharipande
amp Ravenhall PRC 58 1804 (1998))
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS massive NS
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
3bf is poorly known
A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton
A microscopic model is based on a meson exchange model coupled with nucleonic excitations ((1232)N(1440)hellip) consistent with two body interaction
Chiral perturbation theory
Rijkijkijk VVV 2
model IX Urbana
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Carlson et al NP A401(1983) 59
P Grangersquo et al PR C40 (1989)
1040
Microscopic model
(a) excitation of a Δ resonance (attractive)(b) Roper R resonance (repulsive)
(a) excitation of (ΔR) resonances (b) excitation of a nucleon-antinucleon pair (relativistic effect on the EOS repulsive)
Zuo LombardoLejeuneMathiot
N P A706 418 (2002)
Effects of TBF
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
+ + N
+ + N
N
N
+ (-)
Meson-exchange Model of the two and three body Interaction
baryon exc ph exc from Dirac sea
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
+ +
+
N
N
+
N
N
+
+
+
N
N+
N+
(-)
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
BHF vs Dirac-BHFrelativistic effects
but DB misses other TBF effects
impressive overlap
N
BHF + ( ) = DBHF
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
EoS Symmetry energy
Improved saturation point asymp 018 fm-3 Symmetry energy at saturation Svasymp 32 MeV
Incompressibility at saturation K asymp 210 MeV
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Science 298 1592 (2002)
bull Transverse Flow Measurements in Au + Au collisions at EA=05 to 10 GeV
bull Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory
EoS of dense matter from HIC
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
from pure baryon to composite matter
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Composition of Neutron Stars -equilibrium neutral matter
e
e
p e n
p n
e
341
2sym
pF
EY
ck
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Neutron Stars Asymmetric and charge neutral beta-stable matter
Zhou BurgioLombardoZuo PR C69 018801 (2004)
Compact Stars in GTR Tolman-Oppenheimer-Volkoff Equations
Mtheor Mobs
Only stiff EoS is compatible with massive NS (21 Mcopy )
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Yperons
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
INCLUDING HYPERONS
Possible extension of the BBG theory
Few experimental data on NH interaction Nijmegen interaction (NSC89) (Maessen et al Phys Rev C40 2226 (1989))
Unknown HH interaction
Strong consequences for NS structure
See F Burgio et al Phys Rev C583688 (1998) ibid 61 055801 (2000)
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Hyperon onset at density close to 2-3 times the saturation value
Weak dependence on the adopted 3BF
Strong softening of the EoS no matter the nucleonic
TBFrsquos
Hyperon-hyperon interaction
n n n
n n p
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Same results by the Barcelona groupI Vidana et al Phys Rev C73 058801 (2006)
with NSC97 Nijmegen potential (NH + HH inter (Stoks amp Riken1999))
Appearance of baryonic strange matter not compatible with any NS
mass data
It demands for a stiffeningof the Equation of State
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
K condensationBethe-Brown ApJ 1995
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Kmacr - condensation
Proton strangenesscontent a3 ms [MeV]
(a) =-310 (b) =-230 (c) =-134
Chemical equilibrium
n harr p + l + l
n harr p + Kmacr l harr l + Kmacr
nuclear matter npeKhellip2
0( ) (1 2 ) ( )A A l KE K V u u x S u E E
K= e
TBF
ZuoALiZH Li Lombardo PRC 2004
ThorssonLattimer Prakash NPA 1994
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Chemical composition of NS with K-condensation
p
p
K-
K-
e-
e-
Av18 ( thin )
Av18+TBF ( thick )ZuoALiZH Li Lombardo PRC 2004
lsquonuclear matterrsquo starBethe amp BrownApJ 1995
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Critical density c0
2bf 2bf+3bfa3ms=-310 26 24 in competitiowith Yperons =-222 34 29 =-134 50 38
model parameter dependence
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Critical density (u=0)
2bf 2bf+3bf
a3ms=-310 uc=26 24
=-222 =34 29
=-134 = 50 38
K-condensation vs hyperonization
V18 (or Paris)+ TBF the two critical density could be comparable
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Kaon condensantion - neutrino trapping -
-trapping
free
K threshold model dependent
no kaons with kaons
with kaons
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
EoS with phase transitionto K-condensation
ThorssonLattimer Prakash NPA 1994
ZuoALiZH Li F Burgio Lombardo PRC 2006
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
ZuoALiZH Li F Burgio Lombardo PRC 2006
K-condensation in NS Mass-Radius plot
neutrino trapping
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Quark phase
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Structure of Hybrid Stars
at large ( 1 fm-3) hadron phase can coexist with deconfined quark phase and eventually completely dissolve into a pure quark core (hybrid star)
after the recent discovery of massive stars with Mgt2Mcopy (2005)
study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth
the low mass and high mass NS could belong to two different evolutionary scenarios
outlook
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
transition from Hadron to Quark Phase
~1fm3 dNN~ 1 fm
Since we have no unified theory which describes both confined and deconfined phases we use two separate EOS one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Which model for Quark Matter
Constraints from phenomenology on the general quark EOS
i) In symmetric nuclear matter one can expect a transition to quark matter at some density but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate
energy)
ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)A gtgt 03)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than 144 solar mass (not true after 2005 new data with MMcopy gt 2 PSR
J0751+1807 )
Baym amp Chin PLB62 (1976)241Chapline and Nauenberg Nature 264 (1976)Keister amp Kisslinger PLB64(1976)117
c60
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Quark matter models Quark matter models MIT Bag Model MIT Bag Model Nambu-JonamdashLasinio (NJL)Nambu-JonamdashLasinio (NJL) Color Dielectric (CDM)Color Dielectric (CDM) DDM Model DDM Model
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
DDM model from deconfined phase to asymptotic freedom
013
DM Mq q
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
QM vs HM EoS in -equilibrium - crosspoints -
quark matter nb=(Nu+Nd+Ns)3Vnuclear matter = (N+Z) V
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Yperonized NM
Peng and Lombardo PP 2007
d rarr u + e + s rarr u + e + u + s harr d + u
Baryonic NM
Three flavor QM
p + e rarr n + n + n rarr n + n + n harr p + macr
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
hadron-to-quark phase transition
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP = QP THP = TQP
under the total charge neutrality condition
line pHP under H-charge neutrality is the EoS of pure hadron phase line pQP under Q-charge neutrality is the EoS of pure quark phase line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase
n = u + 2 d in he quark phase
hadron-to-quark phase transition
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
NP and QP charge neutrality gives a curve
Peng and Lombardo 2007
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
The value of the maximum mass lies in the range between 15 and 19 solar masses (gt144 M0)
The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS
MIT DDM stable stars are in a quark + mixed + hadronic phase
CDM stable stars are only in pure quark phase
NJL instability at the quark onset
(hadron + mixed phase)
ldquoHybridrdquo starsldquoHybridrdquo stars
C Maieron et al Phys Rev D70 070416 (2004)F Burgio et al Phys Rev C66 025802 (2002)M Buballa et al PLB 562 153 (2003)GX Peng and U Lombardo PP 2007
Quark PhaseHadronic Phase
The structure of neutron star is strongly dependent on the EoS used for describing the quark phase
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
MDD
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Title
X Axis Title
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Two evolutionary scenarios for NS
Haensel exoct 2007 (Catania June 11-15)
NS born in core-collapse of massive stars (20-30 Mcopy ) are sufficiently dense and hot to produce eos-softening quark core resulting in Mmax = 15 M copy
NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to Mmax 2 M copy (no quark core)
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
PSR J0751+1807 M 2102 M
Two evolutionary branches of NS
pure hadron matter
hybrid neutron star
PSR 1913+16 M 14402 M
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Final comments
NS mass is a robust constraint of the nuclear matter EoSthe range 15-20 solar masses predicted by solving theTOVeqs is not trivial
But there are other constraints of the EoS to be investigated
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms URCA opacity pairing
Magnetic field
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Conclusions
The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section
A stiff EoS is also supported by the NS observed masses (and other observables not discussed here) EoS of hadron phase including yperons is reasonably described
EoS of quark phase requires additional study (improving NJL model)
the low mass (Mlt15Mcopy) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons
the high mass (Mgt20Mcopy) is interpreted as pure hadron phase
anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Thank you
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
under charge neutrality condition for the two phases - Maxwell construction -
hadron-to-quark phase transition
no Coulomb no surface
Gibbs equilibrium condition
pHP ( ne) = pQP (ne) HP=QP THP = TQP
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
hadron phase
p + e rarr n + n rarr p + e + n harr p + K
P + e = n
N + P = K
no trapping quark phase
u + e = d
d = s
d rarr u + e + s rarr u + e + u + s harr d + u
one (two) independent variables in each phase if charge neutrality is (not) required
d rarr u + e + s rarr u + e + u + s harr d + u
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Isospin dependence of critical density no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Kaon condensation in pure hadron phase with Skirme-like EoS( the scenario will not significantly change with the BHF+TBF EoS)
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
supernovae explosions (high temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
205 MeV is the threshold for hadron stability against two flavor quark matter
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
0 2 4 6 8 10 12 14 16 18 20
00
02
04
06
08
10
12
14
16
Y A
xis
Titl
e
X Axis Title
M-R plot for Hybrid Stars
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Sensitivity of MMΘ to constant B
MM 0
133 30 135 30 144 20 152 15
Alford amp Reddy2003
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
quark phase in beta-equilibrium udse-
u + e = d
d = s
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
DDM vs MIT-B models
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
charge conservationconservation
0c c c cp eHP K
0c c c c c cu s e KQP d
hadron phase
mixed phase
quark phase
(1 ) 0c cHPQP
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Phase transition from nuclear matter to SQM (skyrme-like EoS)
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
DDM vs MIT
P minimum in DDME=0 in the vacumm
Q matter in beta-equilibrium (charge neutrality)
Quark matter
hadronization(no quarks)
If D12 decreases the crosspointMoves to lower density
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
BaldoBurgioSchulze PRC 61 (2000)
Yperon-rich NS
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
MaieronBaldoBurgioSchulzePhysRev D70 (2004)
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Neutron Star Structure
Clusters and light particle condensatesSuperfluid states
Coexisting liquid-gas phase
Nuclei far from stability line
Hypernuclear matter
K condensation
Quark matter
Hadron-to quark mixed phase
Color superconductivity
Collective excitations
helliphelliphelliphelliphelliphellip
extraordinary laboratory for studying states of nuclear matter
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Table of IsotopesNeutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
nuclear compressibility symmetry energy spin-isospin
from exotic nuclei
Di Toro et al
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq + EoS =P()
mass-radius plotall EoS are consistent with the observed max mass of NS and the central densities are also quite largebut we need a verylarge max mass when including hyperons
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
NS cooling via neutrino emission
p + e- n + e
n p + e- + e
(np) + p + e- (np) + n + e
(np) + n (np) + p + e- + e
direct URCA Yp gt
modified URCA
1
9
The EoS predicts1
9Ypgt gt 028 fm-3
central = 624 fm-3
Direct URCA processes are allowed to occur
