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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) ● 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 ● 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 Cooling (mean free path, heat capacity, conductivity, neutrino emissivity) ● Pulsar kicks ● Magnetic fields ● Proto-neutron stars ● Gamma ray bursts ● 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) ● Christoffel symbols: Гσμν= gσλ (∂νgμλ + ∂μgνλ – ∂λgμν) / 2 ● Riemann tensor: Rτμνσ = ∂νГτμσ – ∂σГτμν + ГκμσГτκν – ΓκμνΓτκσ ● Ricci tensor: Rμν = Rτμσν gστ ● 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 30 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