Transcript Nuclear Incompressibility and Compact Stars

Nuclear Incompressibility and
Compact Stars
Fridolin Weber, San Diego State University
“Neutron” Star
H/He plasma
Outer
crust
?
Inner
crust
M~1.4 Msun, R~10 km
Core
Classical Neutron Star Composition
~ 1930's
Neutrons
Neutron Star Composition in 2005
Influence of
Incompressibility & Symmetry
Energy on NS Properties
●
Core composition (hyperons, bosons, quarks;
superfluid protons, superconducting quarks)
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Neutron star masses (1.25 Msun, 1.7 Msun)
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Fast rotation (Kepler, GW instabilities)
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Do sub-millisecond pulsars exist?
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Superconducting quark matter (CFL, 2SC,
LOFF, ...)
●
●
r-modes
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Signals of phase transitions
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Evolutionary transitions (neutron star to
strange star transition)
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Surface gravity (mass accretion, frame
dragging, red-shifted/blue-shifted
photons)
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Nuclear crust thickness (isolated neutron
stars, LMXBs, pulsar glitches)
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Gravity waves from neutron stars (e.g.,
r-modes, f-modes, ...)
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Stellar cooling
Cooling (mean free path, heat capacity,
conductivity, neutrino emissivity)
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Pulsar kicks
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Magnetic fields
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Proto-neutron stars
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Gamma ray bursts
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X-ray burster
●
....
Selected Neutron Star Masses
J0621+1002: 1.7±0.6 Msun
68% cfl
95% cfl
J0751+1807: 2.1+0.4
Msun
-0.5
J1713+0747: 1.3 +0.9
M
+0.3 sun
B1855+09: 1.6±0.2 Msun
Vela X-1: 2.27± 0.17; 1.88±0.13
J1829+2456: companion mass 1.22 to 1.38 Msun
Vela X-1: 1.88±0.13 Msun, 2.27±0.17 Msun
Cyg X-2: 1.44±0.06 Msun, R=9.0±0.5 km @ 11 kpc
0.97±0.04 Msun, R=7.7±0.4 km @ 9 kpc
J0737-3039: 1.249±0.001 Msun
D. Nice et al. (2004)
Models for the Nuclear Equation of
State
Mass-Radius Relationship of
Neutron and Quark Stars
Quark stars
R~
< 10 km
“Neutron” stars
R>
~ 10 km
Einstein's Field Equations for Rotating Compact Objects
●
Metric: ds2 = − e−2ν dt2 + e2(α+β ) r2 sin2ϑ (dφ – Nφ dt)2 + e2(α–β) (dr2 + r2 dϑ2)
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Christoffel symbols:
Гσμν= gσλ (∂νgμλ + ∂μgνλ – ∂λgμν) / 2
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Riemann tensor:
Rτμνσ = ∂νГτμσ – ∂σГτμν + ГκμσГτκν – ΓκμνΓτκσ
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Ricci tensor: Rμν = Rτμσν gστ
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Scalar curvature: R = Rμν gμν
Kepler frequency: ΩK = r–1 eν–α–β UK + Nφ at r=Req
=> Stellar properties: M, Rp, Req, I, z, ΩK, ω I
Dependence of Particle Thresholds on Spin
Frequency of a Neutron Star
60% change!!
F. Weber, Prog. Nucl. Part.
Phys. 54 (2005) 193-288
Rotation at Mass Shedding Frequency
1.6 ms
PK = 2π/ΩK
= 2π√(R3/M)
“neutron”
stars
CFL
strange quark
stars
Parkes radio telescope
Frame Dragging of the LIFs
Quark-Hadron Composition
(Relativistic Hartree)
Hyperons
Nucleons only
Quark-Hadron Composition
Relativistic Hartree
Relativistic Hartree-Fock
Stellar Composition (M~1.4 Msun)
“Traditional” NS
Quark-hybrid star
Quark-hybrid star
p,n
liquid
p,n
liquid
Density Contours
Quark-Hadron Composition in Rotating
“Neutron” Stars
Equatorial direction
Polar direction
30
10 0
Backbending
ν=65 Hz
(~5 km)
(~3 km)
Glendenning, Pei, Weber,
PRL 79 (1997) 1603
ν=220 Hz
Weber, J. Phys. G: Nucl.
Part. Phys. 25 (1999) R195
Weber, Prog. Part. Nucl.
Phys. 54 (2005) 193
Differentially Rotating Stellar Objects
Ω
1.9
km
M=1.4 Msun
νeq=290 Hz
νc=140 νeq
5.5 km
14.3 km
Open issue: stability?
Pulsar B (1.25 Msun) in J0737-3039
P. Podsiadlowski et al., MNRAS (in press)
My analysis: variational calculation (WUU),
RMF, and RBHF (Brockmann B)
lead to Mby = 1.365 to 1.375 Msun
provided
K=240 MeV
m*/m=0.78
asym=32 MeV
at nuclear matter saturation density.
Summary
Spin Frequency Evolution of
Neutron Stars in LMXB's
Frequency Distribution of X-Ray
Neutron Stars
Glendenning & Weber, ApJ 559 (2001) L119
Histogram of Neutron Stars Spin
Frequencies
(from L. Bildsten, astro-ph/0212004)
Solid line
is for
MSPs in
47 Tuc
Population
decline to
high frequencies in 47 Tuc
Dashed line is for
4U 1916-053
4U 1702-429
4U 1728-34
KS 1731-260
Aql X-1
MXB 1658-298
4U 1636-53
MXB 1743-29
SAX J1750.8-2980
4U 1608-52
Sax J1808.4-3658
XTE J1751-305
XTE J0929-314
Quark-Hadron
Thresholds
Differentially Rotating Stars
Sequences of constant baryon
number
Mass versus Radius Relationships
accreting neutron star
Relativistic Nuclear Field-Theory
L = ΨB(iγμ∂μ – mB) ΨB + Mesons (σ,ω,π,ρ,η,δ,ϕ) + Interactions
Baryons: (iγμ∂μ – mB) ΨB = gσB σ ψB + gωB γμωμψB + ...
Mesons: (∂μ∂μ + mσ2) σ = ΣB gσB ψB ψB
B'1
σ, ω, π, ρ, ...
T=V + ∫ V [g g] T
∑=∫ T g
g = g 0 + g0 ∑ g
B'2
Γ2
Γ1
T matrix
B1
B2
RXJ 1856.5-3754
Discovered serendipitously in study of pre-main-sequence stars in R CrA
star forming region
• Brightest INS candidate in X-rays HST parallax => 110-175 pc
(Walter & Lattimer 2002; Kaplan et al 2002; 175 pc - Kaplan 2003!)
• Proper motion points to Upper Scorpius OB association => age~106yr
●
“Neutron” Star Cooling
CFL?
2SC?
Possible Quark-Hadron Composition
Ω
Braking of Pulsars
Isolated
pulsars
spin down
because
of energy and
angular
momentum
loss due to
radiative
processes
Crab/VLT/ESO
ddE/dt
= d/dt (½ I Ω2) = - C Ωn+1
Braking index: n = (Ω d2Ω/dt2)/(dΩ/dt)2
= 3 – (I'' Ω2+3I' Ω)/(I' Ω+2I)
(I'≡dI/dΩ)
Possible Astrophysical Signal of
Quark Deconfinement
Epoch over which “n” is anomalous
~108 years
About 10%
of the existing
millisecond
pulsar
population
could signal
quark
deconfinement
in their centers!
Neutron Star Temperatures
Dany Page, Seoul, South Korea, 2003 (http://beauty.phys.pusan.ac.kr/~astro/)
Ω
Facts about pulsars:
M~1-2 Msun
● R~10 km
●
} ρ~10
15
g/cm3
P>1.58 ms (630 Hz)
● B~1012 G
● # ~108-1010 (1% MGalaxy)
●
B
Rotating Neutron Star (Pulsar)
Nuclear
Incompressibility
and
Compact Stars
Fridolin Weber
Department of Physics
San Diego State University
JINA Workshop on Nuclear Incompressibility and the Nuclear Equation of State, July 14-15, 2005
Nuclear matter
Quark matter
n
p
Quarks confined inside
neutrons and protons
Unconfined quarks