Nuclear Incompressibility and Compact Stars

							Nuclear Incompressibility and
       Compact Stars
Fridolin Weber, San Diego State University
           “Neutron” Star
                                    H/He plasma




Outer
crust               ?                       Core


   Inner
   crust




              M~1.4 Msun, R~10 km
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;    ●   Signals of phase transitions
    superfluid protons, superconducting quarks)
                                                   ●   Evolutionary transitions (neutron star to
●   Neutron star masses (1.25 Msun, 1.7 Msun)          strange star transition)
●   Fast rotation (Kepler, GW instabilities)       ●   Surface gravity (mass accretion, frame
                                                       dragging, red-shifted/blue-shifted
●   Do sub-millisecond pulsars exist?                  photons)
●   Superconducting quark matter (CFL, 2SC,        ●   Nuclear crust thickness (isolated neutron
    LOFF, ...)                                         stars, LMXBs, pulsar glitches)
     ●   r-modes
                                                   ●   Gravity waves from neutron stars (e.g.,
     ●   Cooling (mean free path, heat capacity,       r-modes, f-modes, ...)
         conductivity, neutrino emissivity)
                                                   ●   Stellar cooling
     ●   Pulsar kicks
     ●   Magnetic fields                           ●   Proto-neutron stars
     ●   Gamma ray bursts                          ●   X-ray burster
                                                   ●   ....
   Selected Neutron Star Masses
                                                     68% cfl
J0621+1002: 1.7±0.6 Msun                   95% cfl

J0751+1807: 2.1+0.4 Msun
               -0.5

J1713+0747: 1.3 +0.9 Msun
                +0.3
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          D. Nice et al. (2004)

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
Models for the Nuclear Equation of
               State
Mass-Radius Relationship of
 Neutron and Quark Stars
   Quark stars   “Neutron” stars
     <
   R ~ 10 km     R > 10 km
                   ~
     Einstein's Field Equations for Rotating Compact Objects

●   Metric: ds2 = − e−2ν dt2 + e2(α+β ) r2 sin2ϑ (dυ – Nυ 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 + Nυ 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    “neutron”
                                   stars
PK = 2π/ΩK
   = 2π√(R3/M)

                           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
M=1.4 Msun                       km
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   Dashed line is for
                             is for       4U 1916-053
                             MSPs in      4U 1702-429
                             47 Tuc       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
                   Population             Sax J1808.4-3658
                                          XTE J1751-305
                   decline to             XTE J0929-314
                   high frequen-
                   cies in 47 Tuc
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                                B'2
                                                         σ, ω, π, ρ, ...
   T=V + ∫ V [g g] T                               Γ1                      Γ2
                                                         T matrix
   ∑=∫ T g                                   B1                                 B2

   g = g 0 + g0 ∑ g
                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



               d E/dt
               d        = 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


                            About 10%
                            of the existing
                            millisecond
              ~108 years    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   Unconfined quarks
 neutrons and protons