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Nuclear Isovector Equation-of-State (EOS)
and Astrophysics
Hermann WolterDep. f. Physik, LMU
Topics:
1. Phase diagram of strongly interacting matter and exploration via heavy ion collisions
2. Symmetric and asymmetric EoS, density dependence of symmetry energy
3. Description of Heavy Ion collisions with transport equations
4. Some results from HI studies
5. Comparison to neutron star observables
6. Summary and Outlook
Connection to Universe Cluster
EoS, esp. Symmetry energy at high density
Interpretation of heavy ion collision exp.
(Astrophysical reaction rates by indirect methods)
Schematic Phase Diagram of Strongly Interacting Matter
Quark-hadron coexistence
Liquid-gas coexistenceSIS
Schematic Phase Diagram of Strongly Interacting Matter
Liquid-gas coexistence
Quark-hadron coexistence
Z/N
1
0
SIS
neutron starsExotic nuclei
Theoretical Treatment of Nuclear Matter
Vij
Non-relativistic:
Hamiltonian H = Ti + Vij,; V nucleon-nucleon interaction
Comparisons of calculations:
Empirical saturation point
Relativistic:
Hadronic Lagrangian
nucleon, resonances
mesons 0
,...),,,,;(
,
ii
L
dx
dL
L
The nuclear EoS-UncertaintiesThe nuclear EoS-Uncertainties
stiff
soft
C. Fuchs, H.H. Wolter, WCI book, EPJA 30 (2006 )5
the nuclear EoS
iso-stiff
iso-soft
Symmetry energy
Esym
m
[MeV
]
Transport Descriptions of Heavy Ion Collisions
Heavy ion collisions -> Non-Equilibrium Phenomena -> Transport Theory
Transport description of heavy ion collisions:
For Wigner transform of the one-body density: f(r,p;t)
,fIfUfm
p
t
fcollp
Vlasov eq.; mean field 2-body hard collisions
)1)(1()1)(1(
)()()2(
1
432432
432143213412
124322
3
ffffffff
EEEEppppd
dvdpdpdp
loss term gain term
11 1
12
3 4
AN
iii tppgtrrg
Ntprf
1
))((~))((1
);,(
Simulation with Test Particles:
Hamiltonian EoM test particles
High Density
Symmetric Nuclear Matter
Observables
V2: Elliptic flowV1: Sideward flow
...2cos),(cos),(1(),,;(: 210 ttt pyvpyvNbpyNFlow
T.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)
Isospin Transport through Neck:
AMeVSnSn 50,124,112124,112
Rami imbalance ratio:
,...,,,;,;2
3112112124124
112112124124
Het
ZNITPi
II
IIIR
ii
iiMi
i
asysoft eos superasystiff eos
experimental data(B. Tsang et al. PRL 92 (2004) )
ASYSOFT EOS – FASTER EQUILIBRATION
Baran, Colonna, Di Toro, Zielinska-Pfabe, Wolter, PRC 72 (2005) 064620
Kaon Production:
A good way to determine the symmetric EOS (C. Fuchs, A.Faessler, et al., PRL 86(01)1974)
Also useful for Isovector EoS?
-charge dependent thresholds
- in-medium effective masses
-Mean field effects
Main production mechanism: NNBYK, pNYK
Astrophysical Implications of Iso-Vector EOS
Neutron Star Structure
Constraints on the Equation-of-state
- from neutron stars: maximum mass
gravitational mass vs.
baryonic mass
direct URCA process
mass-radius relation
- from heavy ion collisions: flow constraint
kaon producton
Equations of State tested:
Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802
Neutron star masses and cooling and iso-vector EOS
Tolman-Oppenheimer-Volkov equation to determine mass of neutron star
Proton fraction and direct URCA
cooling neutrinofast %,11 :ld thresho
:processURCA direct
)( :neutrality charge and mequilibriu
y
enp
yZ
N y
e
sym
Onset of direct URCA
Forbidden by Direct URCA constraint
Typical neutron stars
Heaviest observed neutron star
Further Neutron Star Constraints:
Mass-Radius Relation:
Gravitational vs. Baryon Mass
Max
imu
m m
ass
Dir
ect
Urc
a C
oo
lin
g l
imit
Mas
s-R
adiu
s R
elat
ion
s
Gra
vita
tio
nal
vs.
Bar
yon
M
ass
Hea
vy I
on
Co
llis
ion
o
bse
vab
les
Summary and Outlook:
1. Equation of State at high densities can be tested in the laboratory in heavy ion collisions
2. Symmetry Energy (neutron matter) is particularly uncertain
3. Is important for the structure of exotic nuclei (nucleosynthesis) and for astrophysics
4. Comparison to neutron star observables (not completely satisfactory, yet); also supernovae
Collaborators:
C. Fuchs (Tübingen), T. Gaitanos (Giessen)
D. Blaschke, et al., (Rostock-Breslau)
M. Di Toro, M. Colonna, et al., (LNS Catania)