Neutron stars and quark matter

Gordon Baym

University of Illinois, Urbana

21st Century COE Workshop:Strongly Correlated Many-Body Systems

from Neutron Stars to Cold Atoms

19 January 2006

東京大学

Mass ~ 1.4 Msun

Radius ~ 10-12 kmTemperature ~ 106-109 K

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

Mountains < 1 mm

Density ~ 2x1014g/cm3

Cross section of a neutron star

Properties of matter 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

3

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).

h 0 icondensate

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

Akmal, Pandharipande and Ravenhall, 1998

Mass vs. central density

Mass vs. radius

Maximum neutron star mass

2.2M¯

Accurate for n» n0. n À 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 (fm3).-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?

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

Well beyond nuclear matter density

Onset of new degrees of freedom: mesonic, ’s (-N resonance), quarks and gluons, ... . Properties of matter in this extreme regime determine maximum neutron star mass.Large uncertainties!

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

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

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neutron stars?Solid state physics

Low energy nuclear physics

(1983)

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 quark gluon plasma

Karsch & Laermann, hep-lat/0305025

2nd order

tricritical pt.

1st order

Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)

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

via axial anomaly

Hadronic

Normal

Color SC

(as ms increases)

Predictions of phase transition at finite

Lattice gauge theory

Strong coupling qcdKawamoto et al., hep-lat/0512023

Effective (NJL) theoriesRatti,Thaler,&Weise,

nucl-th/0604025 Nf=2

de Forcrand & Kratochvilahep-lat/0602024

Onset of quark matter at low temperatures difficult to predict via lattice gauge theory. c»5-10nm

Observations of massive neutron stars, M» 2M¯

=> equation of state stiff, and central density so low that sharp transition to bulk quark liquid unlikely.

Quark droplets in nuclear matter.Gradual onset of quark degrees of freedom.

Quark Droplets in Nuclear Matter Glendenning; Heiselberg; Pethick, Ravenhall and Staubo

Favorable to form negativelycharged quark dropletsnu~100, nd~ns~300, R~5fmQ~ -150|e|

at lower densities than quark-hadron transition since they 1) reduce no. of electrons in matter 2) increase fraction of protons in nuclear matter

Neutron stars likely to have such mixed phase cores, butresults are very model dependent

In fact, expect similar pasta phases of quark droplets:

Structure, neutrino emissivity?

a) Masses of neutron stars: equation of state

b) Glitches: probe n,p superfluidity and crust

c) Cooling of n-stars: search for exotica

d) Burst oscillations: probe nuclear physics to ~109g/cm3

Learning about dense matter from neutron star observations

Infer masses from periods and Doppler shifts

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 ± 0.23M¯

Vela X-1: M=1.86 ± 0.15M¯ allow some softening

PSR J0751+1807: M » 2.1 M¯ no softening

QPO 4U1820-30: M » 2.2-2.3 M¯ challenge microscopic e.o.s.

Measured neutron star masses in radio pulsarsThorsett and Chakrabarty, Ap. J. 1998

neutron star - neutron starbinaries

M=1.350.04M¯

Hulse-Taylor

1.18M¯ < M < 1.44M¯

Hulse-Taylor binary

Measured neutron star masses in radio pulsars

(from I. Stairs)

Possible path to compact binary system (Bart & Kalogera)

NICE

22-ms pulsar J07373039A

+2.7-sec pulsar J07373039B companion

orbital period = 2.4 hours!

NEW BINARY PULSAR SYSTEM Lyne et al., Science 303, 1153 (2004)

Highly-relativistic double-neutron-star system

See eclipsing of A by B

Laboratory for gravitational physics!

See orbit almost edge-on:

Mass determinations:

Stellar masses A=1.337(5)M¯ , B=1.250(5)M¯

Vela X-1 (LMXB) light curves Serious deviation from Keplerian radial velocityExcitation of (supergiant) companion atmosphere?

1.4M¯

1.4M¯

M=1.86 0.33 (2)M¯

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

1.75M¯<M<2.44M¯

Quaintrell et al., A&A 401, 313 (2003)

PSR J0751+1807 3.4 ms. pulsar in circular 6h binary w. He white dwarf

Nice et al., Ap.J. 634, 1242 (2005)

M=2.1M¯

Pulsar slowing down due to gravitational radiation: dP/dt = 6.4£10-14

Shapiro delay of signal due to gravitational field of companion: t = - (2Gm2/c3) ln(1-cos) = angle between ns and wd seen by observerMeasurements free (?) of uncertainties from possible atmospheric distortion in companion

Additional physics that allows one to pin down the masses

from D. Nice

Neutron star (pulsar) - white dwarf binaries

Nice et al., Ap.J. 634, 1242 (2005), Splaver et al., Ap.J 620, 405 (2005).

Observations of white dwarf companionC. G. Bassa, van Kerkwijk, & Kulkarni, astro-ph/0601205

Companion is very red: Teff » 4000K. Implies w.d. has He or He-H atmosphere.

Two mysteries:

1) Evolutionary models suggest companion should havehot (burning) H atmosphere.

2) The pulsar does not seem to heat the w.d. atmosphere.Absorbed and re-emitted radiation < 15%.

Need more detailed observations of spectra of white dwarf

Neutron-Star Low Mass X-ray Binaries

X-ray flux power density spectrumWijnands et al. (1998)

Kilohertz quasiperiodic oscillations (QPOs) in accreting neutron stars

Detected in ~ 25 neutron stars

QPOs remarkably coherent (Q =/d ~ 30–200)

Large amplitude

Usually see 2 simultaneous kHz QPOs (never 3)

Frequencies of the two QPOscan vary by hundreds of Hz in few hundred seconds, but

Separation QPO = QPO2 -QPO1 of the two QPOs fairly constant ≈ spin or ≈ spin/2

Sco X-1

Strong evidence that higher frequency QPO2 is the ISCO frequency, Then have direct measurement of neutron star mass:

M*= c3/(63/2£ 2QPO2 G

2198/ QPO2(Hz) )M¯

R c/(6£ 2QPO2)

Ex.: QPO 4U1820-30, QPO2 = 1170 Hz => M~ 2.2-2.3 M¯

innermost circular stable orbit (ISCO)in GR: R=6MG/c2

Implies very stiff equation of state. Central density ~ 1.0 fm-3 ~ 6nm

(Miller, Lamb, & Psaltis 1997)

EXO0748-676: low mass x-ray binary thermonuclear burst source

z=redshift of Fe and O lines

hypothetical star: 1.8M¯, R=10km

M ' 2.1§ 0.28 M¯

R ' 13.8 § 1.8 km

F. Özel, astro-ph//0605106

Akmal, Pandharipande and Ravenhall, 1998

Present observations of neutron stars masses M ' Mmax ' 2.2 M¯ beginning 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 seemingly 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 possible, only if quark matter is very stiff.

»

»

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

Mc

max = (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¯

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 (cf. EXO0748-676).

Gradual onset of quark degrees of freedomQuarks degrees of freedom -- not accounted for by nucleons interacting via static potentials -- expected to play role.

As nucleons begin to overlap, matter percolates at

(Quarks can still be bound even if deconfined!)

Transition to quark matter likely crossover at low T

nperc » 0.34 (3/4 rn3)

HadronicNormal

Color SCHatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)

Gradual onset of quark degrees of freedomQuarks degrees of freedom -- not accounted for by nucleons interacting via static potentials -- expected to play role.

As nucleons begin to overlap, matter percolates at

(Quarks can still be bound even if deconfined!)

Transition to quark matter likely a crossover at low T

nperc » 0.34 (3/4 rn3)

HadronicNormal

Color SCHatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)