Neutron stars and the properties of matter at high density

Gordon Baym, University of Illinois

Future Prospects of Hadron Physics at J-PARC and Large Scale Computational Physics’

11 February 2012

Mass ~ 1.4-2 Msun

Radius ~ 10-12 kmTemperature ~ 106-109 K

Surface gravity ~1014 that of EarthSurface binding~ 1/10 mc2

Density ~ 2x1014g/cm3

Neutron star interiorNeutron star interiorMountains < 1 mm

Masses ~ 1-2 MBaryon number ~ 1057

Radii ~ 10-12 kmMagnetic fields ~ 106 - 1015G

Made in gravitational collapse of massive stars (supernovae)

Central element in variety of compact energetic systems: pulsars, binary x-ray sources, soft gamma repeatersMerging neutron star-neutron star and neutron star-black hole sources of gamma ray burstsMatter in neutron stars is densest in universe: up to ~ 5-10 0 (0= 3X1014g/cm3 = density of matter in atomic nuclei) [cf. white dwarfs: ~ 105-109 g/cm3] Supported against gravitational collapse by nucleon degeneracy pressure

Astrophysical laboratory for study of high density matter complementary to accelerator experiments What are states in interior? Onset of quark degrees of freedom! Do quark stars, as well as strange stars exist?

The liquid interior

Neutrons (likely superfluid) ~ 95% Non-relativisticProtons (likely superconducting) ~ 5% Non-relativisticElectrons (normal, Tc ~ Tf e-137) ~ 5% Fully relativistic

Eventually muons, hyperons, and possibly exotica: pion condensation kaon condensation quark droplets bulk quark matter

Phase transition from crust to liquid at nb 0.7 n0 0.09 fm-3

or = mass density ~ 2 X1014g/cm3

n0 = baryon densityin large nuclei 0.16 fm-3

1fm = 10-13cm

Properties of liquid interior near nuclear matter density

Determine N-N potentials from - scattering experiments E<300 MeV - deuteron, 3 body nuclei (3He, 3H) ex., Paris, Argonne, Urbana 2 body potentialsSolve Schrödinger equation by variational techniques

Two body potential alone:

Underbind 3H: Exp = -8.48 MeV, Theory = -7.5 MeV 4He: Exp = -28.3 MeV, Theory = -24.5 MeV

Large theoretical extrapolation from low energy laboratory nuclear physics at near nuclear matter density

Importance of 3 body interactions

Attractive at low density

Repulsive at high density

Stiffens equation of state at high densityLarge uncertainties

Various processesthat lead to threeand higher bodyintrinsic interactions(not described by iterated nucleon-nucleoninteractions).

Three body forces in polarized pd and dp scattering 135 MeV/A (RIKEN) (K. Sekiguchi 2007)

Blue = 2 body forces Red = 2+3 body forces

0 condensate

Energy per nucleon in pure neutron matterAkmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804

0 condensate

Energy per nucleon in pure neutron matterMorales, (Pandharipande) & Ravenhall, in progress

AV-18 + UIV 3-body (IL 3-body too attractive) Improved FHNC algorithms. Two minima!E/A slightly higher than Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804

Akmal, Pandharipande and Ravenhall, 1998

Mass vs. central density

Mass vs. radius

Maximum neutron star mass

Equation of state vs. neutron star structure

from J. Lattimer

Accurate for n~ n0. n >> n0:

-can forces be described with static few-body potentials?

-Force range ~ 1/2m => relative importance of 3 (and higher) body forces ~ n/(2m)3 ~ 0.4n fm-3.

-No well defined expansion in terms of 2,3,4,...body forces.

-Can one even describe system in terms of well-defined ``asymptotic'' laboratory particles? Early percolation of nucleonicvolumes!

Fundamental limitations of equation of state based on nucleon-nucleon interactions alone:

Fukushima & Hatsuda, Rep. Prog. Phys. 74 (2011) 014001

Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)Yamamoto, Hatsuda, Tachibana & GB, PRD76, 074001 (2007) GB, Hatsuda, Tachibana, & Yamamoto. J. Phys. G: Nucl. Part. 35 (2008) 10402Abuki, GB, Hatsuda, & Yamamoto,Phys. Rev. D81, 125010 (2010)

New critical point in phase diagram: induced by chiral condensate – diquark pairing coupling via axial anomaly

Hadronic

Normal QGP

Color SC

(as ms increases)

BEC-BCS crossover in QCD phase diagramJ. Phys.G: Nucl. Part. Phys. 35 (2008)

Normal

Color SC

(as ms increases)

BCS paired quark matter

BCS-BEC crossoverHadrons

Hadronic

Small quark pairs are “diquarks”

Model calculations of phase diagram with axial anomaly, pairing, chiral symmetry breaking & confinement

NJL alone: H. Abuki, GB, T. Hatsuda, & N. Yamamoto, PR D81, 125010 (2010).NPL with Polyakov loop description of confinement: P. Powell & GB, arXiv:1111.5911

Couple quark fields together with effective 4 and 6 quark interactions:

At mean field level, effective couplings of chiral field φ and pairing field d:

PNJL phase diagram

Spatially ordered chiral transition = quarkyonic phase Kojo, Hidaka, Fukushima, McLerran, & Pisarski ,arXiv:1107.2124

Structure deduced in limit of large number of colors, Nc

Well beyond nuclear matter density

Hyperons: , , ...Meson condensates: -, 0, K-

Quark matter in droplets in bulkColor superconductivityStrange quark matter absolute ground state of matter?? strange quark stars?

Onset of new degrees of freedom: mesonic, ’s, quarks and gluons, ... Properties of matter in this extreme regime determine maximum neutron star mass.

Large uncertainties!

Hyperons in dense matter

Produce hyperon X of baryon no. A and charge eQ when An - Qe > mX (plus interaction corrections)

Djapo, Schaefer & Wambach, PhysRev C81, 035803 (2010)

Pion condensed matter

Softening of collective spin-isospin oscillation of nuclear matter

Above critical density have transition to new state withnucleons rotated in isospin space:

with formation of macroscopic pion field

Strangeness (kaon) condensates

Analogous to condensateChiral SU(3) X SU(3) symmetry of strong interactions => effective low energy interaction

Kaplan and Nelson (1986),Brown et al. (1994)

“Effective mass” term lowers K energies in matter

=> condensation

=>

Lattice gauge theorycalculations of equationof state of QGP

Not useful yet for realistic chemicalpotentials

Learning about dense matter from neutron star observations

Masses of neutron stars Binary systems: stiff eos Thermonuclear bursts in X-ray binaries => Mass vs. Radius, strongly constrains eos

Glitches: probe n,p superfluidity and crust

Cooling of n-stars: search for exotica

Learning about dense matter from neutron star observations

Dense matter fromneutron star mass determinations

Softer equation of state =>lower maximum mass andhigher central density

Binary neutron stars ~ 1.4 M consistent with soft e.o.s.

Cyg X-2: M=1.78 ± 0.23 M

Vela X-1: M=1.86 ± 0.33M allow some softening

PSR J1614-2230 M=1.97 ± 0.04M allows no softening;

begins to challenge microscopic e.o.s.

Neutron Star Masses ca. 2007

Vela X-1 (LMXB) light curves

Serious deviation from Keplerian radial velocityExcitation of (supergiant) companion atmosphere?

1.4 M

1.4 M

M=1.86 ± 0.33 M ¯

M. H. van Kerkwijk, astro-ph/0403489

1.7 M <M<2.4 M Quaintrell et al.,

A&A 401, 313 (2003)

Highest mass neutron star, PSR J1614-2230-- in neutron star-white dwarf binary

Spin period = 3.15 ms; orbital period = 8.7 dayInclination = 89:17o ± 0:02o : edge onMneutron star =1.97 ± 0.04M ; Mwhite dwarf = 0.500 ±006M

(Gravitational) Shapiro delay of light from pulsar when passing the companion white dwarf

Demorest et al., Nature 467, 1081 (2010); Ozel et al., ApJ 724, L199 (2010.

Highest mass neutron star

M= 1.97±0.04 M

Akmal, Pandharipande and Ravenhall, 1998

Can Mmax be larger?

Larger Mmax requires larger sound speed cs at lower n.

For nucleonic equation of state, cs -> c at n ~ 7n0.

Further degrees of freedom, e.g., hyperons, mesons, or quarks at

n ~ 7n0 lower E/A => matter less stiff.

Stiffer e.o.s. at lower n => larger Mmax. If e.o.s. very stiff beyond

n = 2n0, Mmax can be as large as 2.9 M .

Stiffer e.o.s. => larger radii .

Measuring masses and radii of neutron stars in thermonuclear bursts in X-ray binaries

Time (s)

Measurements of apparent surface area, & flux at Eddington limit(radiation pressure = gravity), combined with distance to star constrains M and R.

Ozel et al., 2006-20l2

Apparent Radius

EddingtonLuminosity

EXO 1745-248 in globular cluster Terzan 5, D = 6.30.6 kpc (HST)

Mass vs. radius determination of neutron stars in burst sourcesOzel et al., ApJ 2009-2011

4U 1608-52 in NGC 66244U 1820-30 in globular cluster NGC 6624, D = 6.8 - 9.6 kpc

KS 1731-260 Galactic bulge source

M vs R from bursts, Ozel at al, Steiner et al.

Ozel, GB, & Guver Steiner, Lattimer, & Brown PRD 82 (2010) Ap. J. 722 (2010) - little stiffer

Results ~ consistent with each other and with maximum mass ~ 2 M

Pressure vs. mass density of cold dense matter inferred from neutron star observations

Fit equation of state with polytropes above

Quark matter cores in neutron stars

Canonical picture: compare calculations of eqs. of state of hadronic matter and quark matter. Crossing of thermodynamic potentials => first order phase transition.

Typically conclude transition at ~10nm -- would not be reached in neutron stars given observation of high mass PSRJ1614-2230 with M = 1.97M => no quark matter cores

ex. nuclear matter using 2 & 3 body interactions, vs. pert. expansion or bag models. Akmal, Pandharipande, Ravenhall 1998

More realistically, expect gradual onset of quark degrees of freedom in dense matter

HadronicNormal

Color SC

nperc ~ 0.34 (3/4 rn

3) fm-3

Quarks can still be bound even if deconfined.

Calculation of equation of state remains a challenge for theorists

New critical point suggeststransition to quark matter is a crossover at low T

Consistent with percolation picture that as nucleons beginto overlap, quarks percolate [GB, Physics 1979]

More realistically, expect gradual onset of quark degrees of freedom in dense matter

HadronicNormal

Color SC

nperc ~ 0.34 (3/4 rn

3) fm-3

Quarks can still be bound even if deconfined.

Calculation of equation of state remains a challenge for theorists

New critical point suggeststransition to quark matter is a crossover at low T

Consistent with percolation picture that as nucleons beginto overlap, quarks percolate [GB, Physics 1979]

Present observations of high mass neutron stars M ~ 2M begin to confront microscopic nuclear physics.

High mass neutron stars => very stiff equation of state,

with nc < 7n0. At this point for nucleonic equation of

state, sound speed cs = ( P/)1/2 c.

Naive theoretical predictions based on sharp deconfinement transition would be inconsistent with presence of (soft) bulk quark matter in neutron stars. Further degrees of freedom, e.g., hyperons, mesons, or quarks at n < 7n0 lower E/A => matter less stiff.

Quark cores would require very stiff quark matter.

Expect gradual onset of quark degrees of freedom.

どうもありがとう

Nuclei before neutron dripe-+p n + makes nuclei neutron rich as electron Fermi energy increases with depth n p+ e- + : not allowed if e- state already occupied_

Beta equilibrium: n = p + e

Shell structure (spin-orbit forces) for very neutron rich nuclei?Do N=50, 82 remain magic numbers? To be explored at rare isotope accelerators, RIKEN, GSI, FRIB, KORIA

Valley of stability

in neutron stars

neutron drip line

No shell effect for Mg(Z=12), Si(14), S(16), Ar(18) at N=20 and 28

Loss of shell structure for N >> Z

even

Neutron Star Models

= mass within radius r

E = energy density = c2

nb = baryon densityP() = pressure = nb

2 (E/nb)/ nb

Equation of state:

Tolman-Oppenheimer-Volkoff equation of hydrostatic balance:

general relativistic corrections

1) Choose central density: (r=0) = c

2) Integrate outwards until P=0 (at radius R)3) Mass of star

Outside material adds ~ 0.1 M¯

Maximum mass of a neutron starSay that we believe equation of state up to mass density but e.o.s. is uncertain beyond

Weak bound: a) core not black hole => 2McG/c2 < Rc

b) Mc = s0Rc d3r (r) (4/3) 0Rc

3

=> c2Rc/2G Mc (4/3) 0Rc3

Mcmax = (3M¯/40Rs¯

3)1/2M¯

Rc) = 0

Mmax 13.7 M¯ £(1014g/cm3/0)1/2

Rs¯=2M¯ G/c2 = 2.94 km

40Rc3/3

Strong bound: require speed of sound, cs, in matter in core not to exceed speed of light:

Maximum core mass when cs = c Rhodes and Ruffini (PRL 1974)

cs2 = P/ c2

WFF (1988) eq. of state => Mmax= 6.7M¯(1014g/cm3/0)1/2

V. Kalogera and G.B., Ap. J. 469 (1996) L61

0 = 4nm => Mmax = 2.2 M¯

2nm => 2.9 M¯

Neutron drip

Beyond density drip ~ 4.3 X 1011 g/cm3 neutron bound states in nuclei become filled. Further neutrons must go into continuum states. Form degenerate neutron Fermi sea.

Neutrons in neutron sea are in equilibrium with those inside nucleus

Protons never drip, but remain in bound states until nuclei merge into interior liquid.

Free neutrons form 1S0 BCS paired superfluid

J. Negele and D. Vautherin, Nucl. Phys. A207 (1973) 298

neutron drip

n p

p

Hartree-Fock nuclear density profiles

Energy per nucleon vs. baryon densityin symmetric nuclear matter

Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804

Quark-gluon plasma

Hadronic matter2SC

CFL

1 GeV

150 MeV

0

Tem

pera

ture

Baryon chemical potential

Neutron stars

?

Ultrarelativistic heavy-ion collisions

Nuclear liquid-gas

Phase diagram of equilibrated quark gluon plasma

Karsch & Laermann, 2003

Critical pointAsakawa-Yazaki 1989.

1st order

crossover