neutron stars and quark matter gordon baym university of illinois, urbana 21 st century coe...
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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
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?
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
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
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!
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
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
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
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)
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