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Transcript of Neutron stars and the properties of matter at high density Gordon Baym, University of Illinois...
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
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:
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
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.
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.
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
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.
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
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