Nuclear Incompressibility and Nuclear Incompressibility and Compact StarsCompact Stars

Fridolin Weber, San Diego State University

?

“Neutron” Star

Outer crust

Inner crust

Core

H/He plasma

M~1.4 Msun

, R~10 km

Neutrons

Classical Neutron Star CompositionClassical Neutron Star Composition ~ 1930's~ 1930's

Neutron Star Composition in 2005Neutron Star Composition in 2005

Influence of Influence of Incompressibility & Symmetry Incompressibility & Symmetry

Energy on NS PropertiesEnergy on NS Properties Core composition (hyperons, bosons, quarks;

superfluid protons, superconducting quarks)

Neutron star masses (1.25 Msun

, 1.7 Msun

)

Fast rotation (Kepler, GW instabilities)

Do sub-millisecond pulsars exist?

Superconducting quark matter (CFL, 2SC, LOFF, ...)

r-modes

Cooling (mean free path, heat capacity, conductivity, neutrino emissivity)

Pulsar kicks

Magnetic fields

Gamma ray bursts

Signals of phase transitions

Evolutionary transitions (neutron star to strange star transition)

Surface gravity (mass accretion, frame dragging, red-shifted/blue-shifted photons)

Nuclear crust thickness (isolated neutron stars, LMXBs, pulsar glitches)

Gravity waves from neutron stars (e.g., r-modes, f-modes, ...)

Stellar cooling

Proto-neutron stars

X-ray burster

. . . .

Selected Neutron Star MassesSelected Neutron Star Masses

J1713+0747: 1.3 Msun

B1855+09: 1.6±0.2 Msun

J0621+1002: 1.7±0.6 Msun

+0.4-0.5

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

+0.3

J0751+1807: 2.1 Msun

+0.9

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)

95% cfl

68% cfl

Models for the Nuclear Equation of Models for the Nuclear Equation of StateState

Mass-Radius Relationship of Mass-Radius Relationship of Neutron and Quark StarsNeutron and Quark Stars

“Neutron” stars R > 10 km

Quark starsR < 10 km~ ~

Metric: ds2 = − e−2ν dt2 + e2(α+β ) r2 sin2ϑ (dφ – Nφ dt)2 + e2(α–β) (dr2 + r2 dϑ2)

Christoffel symbols: Гσ

μν= gσλ (∂

νg

μλ + ∂

μg

νλ – ∂

λg

μν) / 2

Riemann tensor: Rτ

μνσ = ∂

νГτ

μσ – ∂

σГτ

μν + Гκ

μσГτ

κν – Γκ

μνΓτ

κσ

Ricci tensor: Rμν

= Rτμσν

gστ

Scalar curvature: R = Rμν

gμν

Kepler frequency: ΩK = r–1 eν–α–β U

K + Nφ at r=R

eq

Einstein's Field Equations for Rotating Compact ObjectsEinstein's Field Equations for Rotating Compact Objects

I=> Stellar properties: M, R

p, R

eq, I, z, Ω

K, ω

=> Stellar properties: M, R

p, R

eq, I, z, Ω

K, ω

Dependence of Particle Thresholds on SpinDependence of Particle Thresholds on SpinFrequency of a Neutron StarFrequency of a Neutron Star

F. Weber, Prog. Nucl. Part.Phys. 54 (2005) 193-288

60% change!!

Rotation at Mass Shedding FrequencyRotation at Mass Shedding Frequency

PK = 2π/Ω

K

= 2π√(R3/M)

Parkes radio telescope

strange quarkstars

strange quarkstars

“neutron”stars

“neutron”stars

CFL

1.6 ms

Frame Dragging of the LIFsFrame Dragging of the LIFs

Quark-Hadron CompositionQuark-Hadron Composition(Relativistic Hartree)(Relativistic Hartree)

Hyperons Nucleons only

Quark-Hadron CompositionQuark-Hadron CompositionRelativistic Hartree Relativistic Hartree-Fock

Stellar Composition (M~1.4 MStellar Composition (M~1.4 Msunsun))

p,nliquid

p,nliquid

“Traditional” NS Quark-hybrid star Quark-hybrid star

Density ContoursDensity Contours

Quark-Hadron Composition in RotatingQuark-Hadron Composition in Rotating““Neutron” StarsNeutron” Stars

Equatorial direction Polar direction

30

10 0

Backbending

(~5 km)

(~3 km)

Glendenning, Pei, Weber,PRL 79 (1997) 1603

ν=220 Hz

ν=65 Hz

Weber, J. Phys. G: Nucl. Part. Phys. 25 (1999) R195

Weber, Prog. Part. Nucl.Phys. 54 (2005) 193

Open issue: stability?

5.5 km

1.9 km

14.3 km

Differentially Rotating Stellar Objects

Ω

M=1.4 Msun

νeq

=290 Hzν

c=140 ν

eq

Pulsar B (1.25 MPulsar B (1.25 Msunsun) in J0737-3039) in J0737-3039

P. Podsiadlowski et al., MNRAS (in press)

K=240 MeV

m*/m=0.78

asym

=32 MeV

My analysis: variational calculation (WUU),My analysis: variational calculation (WUU), RMF, and RBHF (Brockmann B)RMF, and RBHF (Brockmann B) lead to Mlead to M

byby = 1.365 to 1.375 M = 1.365 to 1.375 Msunsun

provided provided

at nuclear matter saturation density.at nuclear matter saturation density.

SummarySummary

Spin Frequency Evolution of Spin Frequency Evolution of Neutron Stars in LMXB'sNeutron Stars in LMXB's

Frequency Distribution of X-Ray Frequency Distribution of X-Ray Neutron StarsNeutron Stars

Glendenning & Weber, ApJ 559 (2001) L119

Histogram of Neutron Stars Spin Histogram of Neutron Stars Spin FrequenciesFrequencies(from L. Bildsten, astro-ph/0212004)

Solid lineis forMSPs in47 Tuc

Dashed line is for4U 1916-0534U 1702-4294U 1728-34KS 1731-260Aql X-1MXB 1658-2984U 1636-53MXB 1743-29SAX J1750.8-29804U 1608-52Sax J1808.4-3658XTE J1751-305XTE J0929-314

Populationdecline to high frequen-cies in 47 Tuc

Quark-Hadron Quark-Hadron ThresholdsThresholds

Differentially Rotating StarsDifferentially Rotating Stars

Sequences of constant baryon Sequences of constant baryon numbernumber

Mass versus Radius RelationshipsMass versus Radius Relationships

accreting neutron star

Relativistic Nuclear Field-TheoryRelativistic Nuclear Field-TheoryL = Ψ

B(iγμ∂

μ – m

B) Ψ

B + Mesons (σ,ω,π,ρ,η,δ,ϕ) + Interactions

Baryons: (iγμ∂μ – m

B) Ψ

B = g

σB σ ψ

B +

g

ωB γμω

μψ

B + ...

Mesons: (∂μ∂μ + m

σ2) σ = Σ

B g

σB ψ

B ψ

B

T=V + ∫ V [g g] T

∑=∫ T g

g = g0 + g0 ∑ g

=> P(ρ)

T=V + ∫ V [g g] T

∑=∫ T g

g = g0 + g0 ∑ g

=> P(ρ)

σ, ω, π, ρ, ...

B1

B'1 B'

2

B2

Γ1

Γ2

T matrix

RXJ 1856.5-3754RXJ 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 Neutron” Star Cooling

2SC?2SC?

CFL?CFL?

Possible Quark-Hadron CompositionPossible Quark-Hadron Composition

Braking of PulsarsBraking of Pulsars

n = (Ω d2Ω/dt2)/(dΩ/dt)2

= 3 – (I'' Ω2+3I' Ω)/(I' Ω+2I)

n = (Ω d2Ω/dt2)/(dΩ/dt)2

= 3 – (I'' Ω2+3I' Ω)/(I' Ω+2I)

Isolated pulsars spin down becauseof energy and angular momentumloss due to radiative processes

Crab/VLT/ESO

(I'≡dI/dΩ)

ddE/dt = d/dt (½ I Ω2) = - C Ωn+1

Braking index:

Ω

Possible Astrophysical Signal of Possible Astrophysical Signal of Quark DeconfinementQuark Deconfinement

Epoch over which “n” is anomalousEpoch over which “n” is anomalous

~108 years

About 10% of the existingmillisecondpulsar population could signalquark deconfinementin their centers!

Neutron Star TemperaturesNeutron Star Temperatures

Dany Page, Seoul, South Korea, 2003 (http://beauty.phys.pusan.ac.kr/~astro/)

Rotating Neutron Star (Pulsar)

Facts about pulsars:

M~1-2 Msun

R~10 km

P>1.58 ms (630 Hz) B~1012 G # ~108-1010 (1% M

Galaxy)

Facts about pulsars:

M~1-2 Msun

R~10 km

P>1.58 ms (630 Hz) B~1012 G # ~108-1010 (1% M

Galaxy)

ρ~1015 g/cm3

B

Ω

Nuclear Nuclear IncompressibilityIncompressibility

and and Compact StarsCompact Stars

Fridolin WeberDepartment 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

p

n

Unconfined quarksQuarks confined insideneutrons and protons