Loading...

PPT – Neutron star interiors: are we there yet? PowerPoint presentation | free to download - id: 7c2fdf-YjNlY

The Adobe Flash plugin is needed to view this content

Neutron star interiors are we there yet?

Gordon Baym, University of Illinois

Workshop on Supernovae and Gamma-Ray Bursts YIPQS

Kyoto October 28, 2013

Neutron star interior

Mass 1.4-2 Msun Radius 10-12 km Temperature

106-109 K Surface gravity 1014 that of

Earth Surface binding 1/10 mc2

Density 2x1014g/cm3

Nuclei before neutron drip

e-p n n makes nuclei neutron rich

as electron Fermi

energy increases with depth n p e-

n not allowed if e- state already occupied

Beta equilibrium mn mp me

Shell structure (spin-orbit forces) for very

neutron rich nuclei? Do N50, 82 remain magic

numbers? Being explored at rare isotope

accelerators, RIKEN, GSI, FRIB, KORIA

Valley of b stability

in neutron stars

neutron drip line

RIKEN, H. Sakurai 2013

Loss of shell structure for N gtgt Z

even

No shell effect for Mg(Z12), Si(14), S(16),

Ar(18) at N20 and 28

Instability of bcc lattice in the inner crust

D. Kobyakov and C. J. Pethick, ArXiv 1309.1891

BCC Lower energy than FCC or simple

cubic. Predicted (pre-pasta) Coulomb structure at

crust-liquid interface GB, 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 gt kFT screening by electron less

effective.

Critical wavenumber above which pp interaction

is attractive

Most unstable direction determined

from modification 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 ?-ray bursts

in NS mergers, and generation of gravitational

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)

379 Iida, Watanabe and Sato, Prog Theo Phys 106

(2001) 551 110 (2003) 847

Important effects on crust bremsstrahlung of

neutrinos, pinning of n vortices, ...

QMD simulations of pasta phases

Sonoda, Watanabe, Sato, Yasuoka and Ebisuzaki,

Phys. Rev. C77 (2008) 035806

T0

Tgt0

Pasta phase diagram

Properties of liquid interior near nuclear

matter density

Determine N-N potentials from - scattering

experiments Elt300 MeV - deuteron, 3 body

nuclei (3He, 3H) ex., Paris, Argonne, Urbana

2 body potentials Solve Schrödinger equation by

variational techniques

Large theoretical extrapolation from low energy

laboratory nuclear physics at near nuclear

matter density

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

p0 condensate

Neutron star models using static interactions

between nucleons

Maximum neutron star mass

Mass vs. central density

Mass vs. radius

Akmal, Pandharipande and Ravenhall, 1998

Equation of state vs. neutron star structure

from J. Lattimer

Well beyond nuclear matter density

Onset of new degrees of freedom mesonic, Ds,

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?

Hyperons in dense matter

Produce hyperon X of baryon no. A and charge eQ

when Amn - Qme gt mX (plus interaction

corrections). mn baryon chemical potential and

me electron chemical potential

Ex. Relativistic mean field model w. baryon octet

meson fields, w. input from double-?

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.s due to hyperons -- the

hyperon problem. Requires stiff YN interaction.

Fundamental limitations of equation of state

based on nucleon-nucleon interactions alone

Accurate for n n0. n gtgt n0 -can forces be

described with static few-body potentials? -Force

range 1/2m? gt 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

nucleonic volumes!

Lattice gauge theory calculations of equation of

state of QGP Not useful yet for realistic

chemical potentials

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

Demorest et al., Nature 467, 1081 (2010) Ozel et

al., ApJ 724, L199 (2010).

Spin period 3.15 ms orbital period 8.7

day Inclination 8917o 002o edge

on Mneutron star 1.97 0.04M? Mwhite

dwarf 0.500 006M?

(Gravitational) Shapiro delay of light from

pulsar when passing the companion white dwarf

Second high mass neutron star, PSRJ03480432 --

in neutron star-white dwarf binary

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

2013)

Spin period 39 ms orbital period 2.46

hours Inclination 40.2o Mneutron star 2.01

0.04M? Mwhite dwarf 0.172 0.003M?

Significant gravitational radiation 400 Myr to

coalescence!

A third high mass neutron star, PSR J1311-3430 --

in neutron star - flyweight He star binary

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

Mneutron star gt 2.0 M? Mcompanion

0.01-0.016M?

Uncertainties arising from internal dynamics of

companion

Akmal, Pandharipande and Ravenhall, 1998

Mass vs. radius determination of neutron stars in

burst sources

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

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

(No Transcript)

(No Transcript)

Phase diagram of equilibrated quark gluon plasma

Critical point Asakawa-Yazaki 1989.

1st order

crossover

Karsch Laermann, 2003

Quark matter cores in neutron stars

Canonical picture compare calculations of eqs.

of state of hadronic matter and quark matter.

Crossing of thermodynamic potentials gt first

order phase transition.

ex. nuclear matter using 2 3 body interactions,

vs. pert. expansion or bag models. Akmal,

Pandharipande, Ravenhall 1998

Typically conclude transition at ?10?nm --

would not be reached in neutron stars given

observation of high mass PSR J1614-2230 with M

1.97M? gt no quark matter cores

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

014001

K. Fukushima (IPad)

BEC-BCS crossover in QCD phase diagram

GB, T.Hatsuda, M.Tachibana, Yamamoto. J. Phys.

G Nucl. Part. 35 (2008) 10402 H. Abuki, GB,

T. Hatsuda, N. Yamamoto,Phys. Rev. D81, 125010

(2010)

Hadronic

Small quark pairs are diquarks

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 f and pairing field d

PNJL phase diagram

K and K from axial anomaly

Model calculations of neutron star matter and

neutron stars within NJL model

NJL Lagrangian supplemented with universal

repulsive quark-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 masses and

spatially uniform pairing wave functions Smoothly

interpolate from nucleonic equation of state

(APR) to quark equation of state

Neutron star equation of state vs.

phenomenological fits to observed masses and

radii

Lines from bottom to top gV /G 0, 1, 1.5,

5 Cross-hatched region Ozel et

al. (2010) Shaded region Steiner et al. (2010)

Masses and radii of neutron stars vs. central

mass density from integrating the TOV equation

5

1.5

1

gv/G

0

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

well as 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 quark matter

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.

(No Transcript)