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Neutron star interiors: are we there yet?

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Neutron star interiors: are we there yet? Gordon Baym, University of Illinois Workshop on Supernovae and Gamma-Ray Bursts YIPQS Kyoto October 28, 2013 – PowerPoint PPT presentation

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Title: Neutron star interiors: are we there yet?


1
Neutron star interiors are we there yet?
Gordon Baym, University of Illinois

Workshop on Supernovae and Gamma-Ray Bursts YIPQS
Kyoto October 28, 2013
2
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
3
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
4
Valley of b stability
in neutron stars
neutron drip line
5
RIKEN, H. Sakurai 2013
6
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
7
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
8
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.
9
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, ...
10
QMD simulations of pasta phases
Sonoda, Watanabe, Sato, Yasuoka and Ebisuzaki,
Phys. Rev. C77 (2008) 035806
T0
Tgt0
Pasta phase diagram
11
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
12
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
13
Energy per nucleon in pure neutron matter
Akmal, Pandharipande and Ravenhall, Phys. Rev.
C58 (1998) 1804
p0 condensate
14
Neutron star models using static interactions
between nucleons
Maximum neutron star mass
Mass vs. central density
Mass vs. radius
Akmal, Pandharipande and Ravenhall, 1998
15
Equation of state vs. neutron star structure
from J. Lattimer
16
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?
17
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.
18
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!
19
Lattice gauge theory calculations of equation of
state of QGP Not useful yet for realistic
chemical potentials
20
Learning about dense matter from neutron star
observations
Challenges to nuclear theory!!
21
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
22
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!
23
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
24
Akmal, Pandharipande and Ravenhall, 1998
25
Mass vs. radius determination of neutron stars in
burst sources
M vs R from bursts, Ozel at al, Steiner et al.
26
J. Poutanan, at Trento workshop on Neutron-rich
matter and neutron stars, 30 Sept. 2013
27
Or perhaps overestimated, since
R. Rutledge, at Trento workshop on Neutron-rich
matter and neutron stars, 30 Sept. 2013
28
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29
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30
Phase diagram of equilibrated quark gluon plasma
Critical point Asakawa-Yazaki 1989.
1st order
crossover
Karsch Laermann, 2003
31
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

32
Fukushima Hatsuda, Rep. Prog. Phys. 74 (2011)
014001
33
K. Fukushima (IPad)
34
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
35
Continuous evolution from nuclear to quark
matter K. Masuda, T. Hatsuda, T. Takatsuka,
Ap. J.764, 12 (2013)
36
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
37
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
38
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
39
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)
40
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
41
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
42
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.
43
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