1. Nuclear Incompressibility and Compact Stars Fridolin Weber, San Diego State University

2. ? “Neutron” Star Outer crust Inner crust Core H/He plasma M~1.4 M sun, R~10 km

3. Neutrons Classical Neutron Star Composition ~ 1930's ~ 1930's

4. Neutron Star Composition in 2005

5. 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 ●....

6. Selected Neutron Star Masses J1713+0747: 1.3 M sun B1855+09: 1.6±0.2 M sun J0621+1002: 1.7±0.6 M sun +0.4 -0.5 Vela X-1: 2.27± 0.17; 1.88±0.13 J1829+2456: 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 J0751+1807: 2.1 M sun +0.9 Cyg X-2: 1.44±0.06 M sun, R=9.0±0.5 km @ 11 kpc 0.97±0.04 M sun, R=7.7±0.4 km @ 9 kpc J0737-3039: 1.249±0.001 M sun D. Nice et al. (2004 ) 95% cfl 68% cfl

7. Models for the Nuclear Equation of State

8. Mass-Radius Relationship of Neutron and Quark Stars “Neutron” stars R > 10 km Quark stars R < 10 km ~ ~

9. ● 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

10. Dependence of Particle Thresholds on Spin Frequency of a Neutron Star F. Weber, Prog. Nucl. Part. Phys. 54 (2005) 193-288 60% change!!

11. 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

12. Frame Dragging of the LIFs

13. Quark-Hadron Composition (Relativistic Hartree) Hyperons Nucleons only

14. Quark-Hadron Composition Relativistic Hartree Relativistic Hartree-Fock

15. Stellar Composition (M~1.4 M sun ) p,n liquid p,n liquid “Traditional” NS Quark-hybrid star

16. Density Contours

17. Quark-Hadron Composition in Rotating “Neutron” Stars Equatorial direction Polar direction 3030 10  0

18. Backbending

19. (~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

20. 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

21. Pulsar B (1.25 M sun ) in J0737-3039 P. Podsiadlowski et al., MNRAS (in press)

22. 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 = 1.365 to 1.375 M sun lead to M by = 1.365 to 1.375 M sun provided provided at nuclear matter saturation density.

23. Summary

24. Spin Frequency Evolution of Neutron Stars in LMXB's

25. Frequency Distribution of X-Ray Neutron Stars Glendenning & Weber, ApJ 559 (2001) L119

26. Histogram of Neutron Stars Spin Frequencies Histogram of Neutron Stars Spin Frequencies (from L. Bildsten, astro-ph/0212004) Solid line is for MSPs 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 Population decline to high frequen- cies in 47 Tuc

27. Quark-Hadron Thresholds

29. Differentially Rotating Stars

30. Sequences of constant baryon number

31. Mass versus Radius Relationships

32. accreting neutron star

33. Spin Evolution of Accreting Neutron Stars

34. Models for the Nuclear EoS UV 14 +UVII UV 14 +TNI UV14+UVII UV14+TNI

35. 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

36. 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~10 6 yr

37. “Neutron” Star Cooling 2SC? CFL?

38. Possible Quark-Hadron Composition

39. 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

40. Possible Astrophysical Signal of Quark Deconfinement

41. Epoch over which “n” is anomalous ~10 8 years About 10% of the existing millisecond pulsar population could signal quark deconfinement in their centers!

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

43. RBHF Based on Brockmann-Machleidt OBE Potential B Based on Brockmann-Machleidt OBE Potential B Nuclear matter Nuclear matter Neutron matter Neutron matter

44. 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 ● # ~10 8 -10 10 (1% M Galaxy ) Facts about pulsars: ● M~1-2 M sun ● R~10 km ● P>1.58 ms (630 Hz) ● B~10 12 G ● # ~10 8 -10 10 (1% M Galaxy ) } ρ~10 15 g/cm 3 B Ω

45. 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

46. Nuclear matter Quark matter p n Unconfined quarks Quarks confined inside neutrons and protons