Nuclear Incompressibility and Compact Stars Fridolin Weber, San Diego State University
? “Neutron” Star Outer crust Inner crust Core H/He plasma M~1.4 M sun, R~10 km
Neutrons Classical Neutron Star Composition ~ 1930's ~ 1930's
Neutron Star Composition in 2005
Influence of Incompressibility & Symmetry Energy on NS Properties ● Core composition (hyperons, bosons, quarks; superfluid protons, superconducting quarks) ● Neutron star masses (1.25 M sun, 1.7 M sun ) ● 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, re d-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 Masses J : 1.3 M sun B : 1.6±0.2 M sun J : 1.7±0.6 M sun Vela X-1: 2.27± 0.17; 1.88±0.13 J : companion mass 1.22 to 1.38 M sun Vela X-1: 1.88±0.13 M sun, 2.27±0.17 M sun +0.3 J : 2.1 M sun +0.9 Cyg X-2: 1.44±0.06 M sun, R=9.0± kpc 0.97±0.04 M sun, R=7.7±0.4 9 kpc J : 1.249±0.001 M sun D. Nice et al. (2004 ) 95% cfl 68% cfl
Models for the Nuclear Equation of State
Mass-Radius Relationship of Neutron and Quark Stars “Neutron” stars R > 10 km Quark stars R < 10 km ~ ~
● Metric: ds 2 = − e −2ν dt 2 + e 2(α+β ) r 2 sin 2 ϑ (dφ – N φ dt) 2 + e 2(α–β) (dr 2 + r 2 d ϑ 2 ) ● Christoffel symbols: Г σ μν = g σλ (∂ ν g μλ + ∂ μ g νλ – ∂ λ g μν ) / 2 ● Riemann tensor: R τ μνσ = ∂ ν Г τ μσ – ∂ σ Г τ μν + Г κ μσ Г τ κν – Γ κ μν Γ τ κσ ● Ricci tensor: R μν = R τ μσν g σ τ ● Scalar curvature: R = R μν g μν Kepler frequency: Ω K = r –1 e ν–α–β U K + N φ at r=R eq Einstein's Field Equations for Rotating Compact Objects I => Stellar properties: M, R p, R eq, I, z, Ω K, ω
Dependence of Particle Thresholds on Spin Frequency of a Neutron Star F. Weber, Prog. Nucl. Part. Phys. 54 (2005) % change!!
Rotation at Mass Shedding Frequency P K = 2π/Ω K = 2π√(R 3 /M) Parkes radio telescope strange quark stars strange quark stars “neutron” stars “neutron” stars CFL 1.6 ms
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 M sun ) p,n liquid p,n liquid “Traditional” NS Quark-hybrid star
Density Contours
Quark-Hadron Composition in Rotating “Neutron” Stars Equatorial direction Polar direction 3030 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 M sun ν eq =290 Hz ν c =140 ν eq
Pulsar B (1.25 M sun ) in J P. Podsiadlowski et al., MNRAS (in press)
K=240 MeV m*/m=0.78 a sym =32 MeV My analysis: variational calculation (WUU), RMF, and RBHF (Brockmann B) RMF, and RBHF (Brockmann B) lead to M by = to M sun lead to M by = to M sun provided provided 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 Histogram of Neutron Stars Spin Frequencies (from L. Bildsten, astro-ph/ ) Solid line is for MSPs in 47 Tuc Dashed line is for 4U U U KS Aql X-1 MXB U MXB SAX J U Sax J XTE J XTE J Population decline to high frequen- cies in 47 Tuc
Quark-Hadron Thresholds
Differentially Rotating Stars
Sequences of constant baryon number
Mass versus Radius Relationships
accreting neutron star
Spin Evolution of Accreting Neutron Stars
Models for the Nuclear EoS UV 14 +UVII UV 14 +TNI UV14+UVII UV14+TNI
Relativistic Nuclear Field-Theory L = Ψ B (iγ μ ∂ μ – m B ) Ψ B + Mesons (σ,ω,π,ρ,η,δ, ϕ ) + Interactions Baryons: (iγ μ ∂ μ – m B ) Ψ B = g σB σ ψ B + g ωB γ μ ω μ ψ B +... Mesons: (∂ μ ∂ μ + m σ 2 ) σ = Σ B g σB ψ B ψ B T=V + ∫ V [g g] T ∑=∫ T g g = g 0 + g 0 ∑ g => P(ρ) T=V + ∫ V [g g] T ∑=∫ T g g = g 0 + g 0 ∑ g => P(ρ) σ, ω, π, ρ,... B1B1 B' 1 B' 2 B2B2 Γ1Γ1 Γ2Γ2 T matrix
RXJ ● Discovered serendipitously in study of pre-main-sequence stars in R CrA star forming region Brightest INS candidate in X-rays HST parallax => pc (Walter & Lattimer 2002; Kaplan et al 2002; 175 pc - Kaplan 2003!) Proper motion points to Upper Scorpius OB association => age~10 6 yr
“Neutron” Star Cooling 2SC? CFL?
Possible Quark-Hadron Composition
Braking of Pulsars n = (Ω d 2 Ω/dt 2 )/(dΩ/dt) 2 = 3 – (I'' Ω 2 +3I' Ω)/(I' Ω+2I) n = (Ω d 2 Ω/dt 2 )/(dΩ/dt) 2 = 3 – (I'' Ω 2 +3I' Ω)/(I' Ω+2I) Isolated pulsars spin down because of energy and angular momentum loss due to radiative processes Crab/VLT/ESO (I'≡dI/dΩ) d dE/dt = d/dt (½ I Ω 2 ) = - C Ω n+1 Braking index: Ω
Possible Astrophysical Signal of Quark Deconfinement
Epoch over which “n” is anomalous ~10 8 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(
RBHF Based on Brockmann-Machleidt OBE Potential B Based on Brockmann-Machleidt OBE Potential B Nuclear matter Nuclear matter Neutron matter Neutron matter
Rotating Neutron Star (Pulsar) Facts about pulsars: ● M~1-2 M sun ● R~10 km ● P>1.58 ms (630 Hz) ● B~10 12 G ● # ~ (1% M Galaxy ) Facts about pulsars: ● M~1-2 M sun ● R~10 km ● P>1.58 ms (630 Hz) ● B~10 12 G ● # ~ (1% M Galaxy ) } ρ~10 15 g/cm 3 B Ω
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 p n Unconfined quarks Quarks confined inside neutrons and protons