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Neutron stars and quark matter Gordon Baym University of Illinois, Urbana

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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

Cross section of a neutron star

Mass ~ 1.4 Msun

Radius ~ 10-12 km

Temperature

~ 106-109 K

Surface gravity

~1014 that of Earth

Surface binding

~ 1/10 mc2

Mountains < 1 mm

Density ~ 2x1014g/cm3

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 potentials

Solve Schrödinger equation by variational techniques

3

Two body potential alone:

Underbind 3H: Exp = -8.48 MeV, Theory = -7.5 MeV

4He: Exp = -28.3 MeV, Theory = -24.5 MeV

Importance of 3 body interactions

Attractive at low density

Repulsive at high density

Various processes

that lead to three

and higher body

intrinsic interactions

(not described by

iterated nucleon-nucleon

interactions).

Stiffens equation of state at high density

Large uncertainties

Energy per nucleon in pure neutron matter

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

h p0i

condensate

Maximum neutron star mass

2.2M¯

Mass vs. central density

Mass vs. radius

Akmal, Pandharipande and Ravenhall, 1998

Fundamental limitations of equation of state based on

nucleon interactions alone:

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?

Well beyond nuclear matter density

Onset of new degrees of freedom: mesonic, D’s (p-N resonance), quarks and gluons, ... .

Properties of matter in this extreme regime determine maximum neutron star mass.

Large uncertainties!

Hyperons: S, L, ...

Meson condensates: p-, p0, K-

Quark matter

in droplets

in bulk

Color superconductivity

Strange quark matter

absolute ground state of matter??

strange quark stars?

もしほんの一つ二つクレイジーな仮定をすれば、

あなたは私の言動のすべてが正しいと解るよ。

(1983)

Solid state

physics

neutron stars?

Low energy

nuclear physics

??

Phase diagram of quark gluon plasma

2nd order

tricritical pt.

1st order

Karsch & Laermann, hep-lat/0305025

Normal

Hadronic

Color SC

New critical point in phase diagram:

induced by chiral condensate – diquark pairing coupling

via axial anomaly

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

(as ms increases)

Predictions of phase transition at finite

de Forcrand & Kratochvila

hep-lat/0602024

Lattice gauge theory

Effective (NJL) theories

Ratti,Thaler,&Weise,

nucl-th/0604025 Nf=2

Strong coupling qcd

Kawamoto et al., hep-lat/0512023

Onset of quark matter at low temperatures difficult

to predict via lattice gauge theory. rc»5-10rnm

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 negatively

charged quark droplets

nu~100, nd~ns~300, R~5fm

Q~ -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, but

results are very model dependent

In fact, expect similar pasta phases of quark droplets:

Structure, neutrino emissivity?

Learning about dense matter from neutron star observations

- Masses of neutron stars: equation of state
- Glitches: probe n,p
- superfluidity and crust
- Cooling of n-stars: search for exotica
- Burst oscillations: probe
- nuclear physics to ~109g/cm3

Infer masses from periods and Doppler shifts

Dense matter from

neutron star mass determinations

Softer equation of state =>

lower maximum mass and

higher 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 pulsars

Thorsett and Chakrabarty, Ap. J. 1998

neutron star

- neutron star

binaries

Hulse-Taylor

M=1.35±0.04M¯

1.18M¯ < M < 1.44M¯

Measured neutron star

masses in radio pulsars

(from I. Stairs)

Hulse-Taylor binary

Possible path to compact

binary system (Bart & Kalogera)

NICE

NEW BINARY PULSAR SYSTEM

Lyne et al., Science 303, 1153 (2004)

22-ms pulsar J0737-3039A

+2.7-sec pulsar J0737-3039B companion

orbital period = 2.4 hours!

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¯

1.4M¯

1.4M¯

Vela X-1 (LMXB) light curves

Serious deviation from Keplerian radial velocity

Excitation of (supergiant) companion atmosphere?

M=1.86 ± 0.33 (2s)M¯

M. H. van Kerkwijk,

astro-ph/0403489

1.75M¯<M<2.44M¯

Quaintrell et al.,

A&A 401, 313 (2003)

q

PSR J0751+1807

3.4 ms. pulsar in circular 6h binary w. He white dwarf

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

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

Shapiro delay of signal due to gravitational field of companion:

D t = - (2Gm2/c3) ln(1-cosq)

q = angle between ns and wd seen by observer

Measurements free (?) of uncertainties from possible atmospheric distortion in companion

M=2.1M¯

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 companion

C. 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 have

hot (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

Kilohertz quasiperiodic oscillations (QPOs)

in accreting neutron stars

Detected in ~ 25 neutron stars

QPOs remarkably coherent (Q =n/dn ~ 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 nQPO = nQPO2 -nQPO1of the two QPOs fairly constant ≈ nspin or ≈ nspin/2

Sco X-1

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

innermost circular stable orbit (ISCO)

in GR: R=6MG/c2

Strong evidence that higher frequency nQPO2 is the ISCO frequency, Then have direct measurement of neutron star mass:

M*= c3/(63/2£ 2pnQPO2 G)

=(2198/ nQPO2(Hz) )M¯

R* = c/(61/3£ 2pnQPO2)

(Miller, Lamb, & Psaltis 1997)

Ex.: QPO 4U1820-30, nQPO2 = 1170 Hz => M~ 2.2-2.3 M¯

Implies very stiff equation of state.

Central density ~ 1.0 fm-3 ~ 6rnm

hypothetical star: 1.8M¯, R=10km

z=redshift of Fe and O lines

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.

»

»

Maximum mass of a neutron star

Say that we believe equation

of state up to mass density r0

but e.o.s. is uncertain beyond

r(Rc) = r0

Weak bound:

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

b) Mc = s0Rc d3r r(r) ³ (4p/3) r0Rc3

=> c2Rc/2G ³ Mc ³ (4p/3) r0Rc3

Rs¯=2M¯ G/c2 = 2.94 km

Mcmax = (3M¯/4pr0Rs¯3)1/2M¯

Mmax ³ 13.7 M¯ £(1014g/cm3/r0)1/2

4pr0Rc3/3

Outside material adds ~ 0.1 M¯

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

cs2 = ¶P/¶r£ c2

Maximum core mass when cs = c

Rhodes and Ruffini (PRL 1974)

WFF (1988) eq. of state => Mmax= 6.7M¯(1014g/cm3/r0)1/2

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

r0 = 4rnm => Mmax = 2.2 M¯

2rnm => 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 freedom

Normal

Hadronic

Color SC

Quarks 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)

Hatsuda, Tachibana, Yamamoto & GB,

PRL 97, 122001 (2006)

Gradual onset of quark degrees of freedom

Normal

Hadronic

Color SC

Quarks 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)

Hatsuda, Tachibana, Yamamoto & GB,

PRL 97, 122001 (2006)