Neutron star interiors: are we there yet?

Gordon Baym, University of Illinois

Workshop on Supernovae and Gamma-Ray BurstsYIPQS Kyoto’

October 28, 2013

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

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? Being explored at rare isotope accelerators, RIKEN, GSI, FRIB, KORIA

Valley of stability

in neutron stars

neutron drip line

RIKEN, H. Sakurai 2013

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

Instability of bcc lattice in the inner crustD. Kobyakov and C. J. Pethick, ArXiv 1309.1891

BCC: Lower energy than FCC or simple cubic.Predicted (pre-pasta) Coulomb structure at crust-liquid interfaceGB, H. A. Bethe, C. J. Pethick, Nucl. Phys. A 175, 225 (1971)

But effective finite wavenumber proton-proton interaction strongly modified by screening:

kFT = Thomas-Fermi screening length

For k > kFT screening by electronless effective.

Critical wavenumber above which pp interaction is attractive:

Most unstable direction determined frommodification of elastic constants J. Cahn, Acta Metallurgica 10, 179 (1962)

Possibly leads to BaTiO3 -like structure:

Similar to pasta phases of nuclei,rearrangement of lattice structure affects thermodynamic and transport properties of crust; effects on cooling and glitches, pinning of n vortices, crust bremsstrahlung of neutrinos.

Modifies elastic properties of crust (breaking strains, modes, ...)affect on precursors of γ-ray bursts in NS mergers, and generation ofgravitational radiation.

Pasta Nuclei over half the mass of the crust !!onset when nuclei fill ~ 1/8 of space

Lorentz, Pethick and Ravenhall. PRL 70 (1993) 379Iida, Watanabe and Sato, Prog Theo Phys 106 (2001) 551; 110 (2003) 847

Important effects on crust bremsstrahlung of neutrinos, pinning of n vortices, ...

Sonoda, Watanabe, Sato, Yasuoka and Ebisuzaki, Phys. Rev. C77 (2008) 035806QMD simulations of pasta phases

T=0

0.10 0.20 0.39 0.49 0.58

T>0

Pasta phase diagram

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).

0 condensate

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

Neutron star models using static interactions between nucleons

Equation of state vs. neutron star structure

from J. Lattimer

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).n = baryon chemical potential and e = electron chemical potential

Ex. Relativistic mean fieldmodel w. baryon octet + meson fields, w. input from double-Λ hypernuclei.Bednarek et al., Astron & Astrophys 543 (2012) A157

Y = number fraction vs. baryon density

Significant theoretical uncertainties in forces!

Hard to reconcile large mass neutron stars with softening of e.o.sdue to hyperons -- the hyperon problem. Requires stiff YN interaction.

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:

Lattice gauge theorycalculations of equationof state of QGP

Not useful yet for realistic chemicalpotentials

Learning about dense matter from neutron star observations

Challenges to nuclear theory!!

High 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).

Second high mass neutron star, PSRJ0348+0432 -- in neutron star-white dwarf binary

Spin period = 39 ms; orbital period = 2.46 hoursInclination =40.2o Mneutron star =2.01 ± 0.04M ; Mwhite dwarf = 0.172 ±0.003M

Significant gravitational radiation

400 Myr to coalescence!

Antonidas et al., Science 340 1233232 (April 26, 2013)

A third high mass neutron star, PSR J1311-3430 -- in neutron star - flyweight He star binary

Mneutron star > 2.0 M ; Mcompanion ~ 0.01-0.016M

Romani et al., Ap. J. Lett., 760:L36 (2012)

Uncertainties arising from internal dynamics of companion

Akmal, Pandharipande and Ravenhall, 1998

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

Mass vs. radius determination of neutron stars in burst sources

J. Poutanan, at Trento workshop on Neutron-rich matter and neutron stars, 30 Sept. 2013

Or perhaps overestimated, since

R. Rutledge, at Trento workshop on Neutron-rich matter and neutron stars, 30 Sept. 2013

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

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

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

K. Fukushima (IPad)

BEC-BCS crossover in QCD phase diagram

Normal

Color SC

(as ms increases)

BCS paired quark matter

BCS-BEC crossoverHadrons

Hadronic

Small quark pairs are “diquarks”

GB, T.Hatsuda, M.Tachibana, & Yamamoto. J. Phys. G: Nucl. Part. 35 (2008) 10402H. Abuki, GB, T. Hatsuda, & N. Yamamoto,Phys. Rev. D81, 125010 (2010)

Continuous evolution from nuclear to quark matter

K. Masuda, T. Hatsuda, & T. Takatsuka, Ap. J.764, 12 (2013)

Hadron-quark crossover equation of state K. Masuda, T. Hatsuda, &T. Takatsuka, Ap. J.764, 12 (2013)

Neutron matter at low density with smooth interpolation to Nambu Jona-Lasinino model of quark matter at high density

quark content vs. density E.o.s. with interpolation between 2 - 4

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 PR D 85, 074003 (2012)

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:

K and K’ from axial anomalyPNJL phase diagram

Model calculations of neutron star matter and neutron stars within NJL model

NJL Lagrangian supplemented with universal repulsivequark-quark vector coupling

K. Masuda, T. Hatsuda, & T. Takatsuka, Ap. J.764, 12 (2013) GB, T. Hatsuda, P. Powell, ... (to be published)

Include up, down, and strange quarks with realistic massesand spatially uniform pairing wave functions

Smoothly interpolate from nucleonic equation of state (APR) to quark equation of state:

0

5

1

1.5

pres

sure

baryon density mass density

Neutron star equation of state vs. phenomenologicalfits to observed masses and radii

Lines from bottomto top:gV /G = 0, 1, 1.5, 5

Cross-hatchedregion = Ozel et al.(2010)

Shaded region =Steiner et al. (2010)

Masses and radii of neutron stars vs. central mass densityfrom integrating the TOV equation

0

1

1.5

5

gv/G=

Mass vs. central density:only stars on rising curves are stable

M vs. R: only stars on rapidly rising curves are stable

Maximum neutron star mass vs. gV

PNJL accomodates large mass neutron stars as wellas strange quarks -- avoiding the “hyperon problem”-- and is consistent with observed masses and radiii

But we are not quite there yet:

Uncertainties in interpolating from nuclear matter to quarkmatter lead to errors in maximum neutron star masses and radii.

Uncertainties in the vector coupling gv

The NJL model does not treat gluon effects well, which leads to uncertainties in the “bag constant” B of quark matter:

At very high baryon density, the energy density is

E = B + Cpf4 ,

with B ~ 100-200 MeV/fm3. Then the pressure is

P = -B + Cpf4 /3.

Effect of B on maximum neutron star mass?

Need to calculate gluon contributions accurately to pin down B.

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