Thermal Evolution of Rotating neutron Stars and Signal of Quark Deconfinement Henan University, Kaifeng, China Miao Kang

 Model of neutron stars(hybrid stars)  The energy release of quark deconfinement  Thermal evolution of hybrid stars and quark deconfinement signature  Conclusion and Discussion

Model of hybrid stars Maxwell construction (a sharp transition takes place between the two charge-neutral hadron and quark phase) ( Baym & Chin,1976,Phys.Lett.B, 62,241 ) Gibbs construction (the transition can occur through the formation of a mixed phase of hadron matter and quark matter, total charge neutrality being achieved by a positively charged amount of hadron matter and a negatively charged amount of quark matter) ( Glendenning N. K., 1992, Phys. Rev. D, 46,1274 )

Model of hybrid stars Gibbs condition at zero temperature between hadron phase and quark phase

Equation of state (EOS) Quark matter Composition: u,d,s,e Model: effective mass bag model considering medium effect(MIT) Idea: quasi-particle approximation Parameters: bag constant B, coupling constant g, the current mass of s quark m s ( Schertler et al. Nucl.Phys.A(1997) )

Equation of state (EOS) Hadron matter Composition: n,p,e, Model: subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS (Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J, (1971)) nuclear densities: Argonne EOS (Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998)) the nucleon interaction with the inclusion of a parameterized three-body force and relativistic boost corrections Composition: n,p,e, Model: subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS (Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J, (1971)) nuclear densities: Argonne EOS (Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998)) Composition: n,p,e, Model: subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS (Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J, (1971)) nuclear densities: Argonne EOS (Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998)) Composition: n,p,e, Model: subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS (Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J, (1971)) nuclear densities: Argonne EOS(APR) (Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998))

Equation of state (EOS) B=85,108,136 g=3.0 M s =150.0MeV

Structure evolution of hybrid stars Static configuration TOV equation (Oppenheimer & Volkoff Phys.Rev,55 374(1939))

Structure evolution of hybrid stars static Maximum rotation frequency Rotation configuration Perturbative Approach (Hartle J. B., 1967, ApJ, 150, 1005) Quark deconfinement Nucleon direct Urca process B=108

Energy release of deconfinement Non-linear dissipation (Professor Zheng xiaoping) The deconfine phase transition from hadron matter to quark matter may continuously occurs during spin-down of NSs. The density of any given fluid element increases, changing its equilibrium state. The relaxation toward the new equilibrium appears accordingly if the transition has nonlinear phase structure by Gibbs construction. So the two phases are not quite equilibrium and binding energy is stored that can be released by phase transition.

Energy release of deconfinement Energy release per baryon The total heat luminosity The simple parameterized form 0.1MeV

Energy release of deconfinement The number of quarks converting into baryons Kang M., Zheng X. P., 2007, MNRAS, 375,1503

Neutrino emission Hadron matter: nucleon direct Urca (NDU) nucleon modified Urca(NMU) nucleon bremsstrahlung(NB) Quark matter: quark direct Urca (QDU) quark modifiedUrca (QMU) quark bremsstrahlung(QB) Glen & Sutherland 1980 Heat capacity Neutrino emission luminosity Surface photon luminosity

Thermal evolution of hybrid stars A quite clear magnetic-field dependence Deconfinement heating can produce a characteristic rise of surface temperature Deconfinement heating dominate the behavior of thermal evolution Low magnetic field (B=10^9G) produces a sharp jump in surface temperature 1.6 solar mass

Thermal evolution of hybrid stars deconfinement heating delay the cooling observational data can be explained well Magnetic B m =10^12,10^11 Gauss Without DH

Thermal evolution of hybrid stars Magnetic B m =10^9,10^8 Gauss High temperatures of stars at older ages(>10^9) yrs A period of increase of surface temperature A evidence of existence of deconfinement quark matter?

Conclusion Explore the signal of quark matter appearing through theoretical simulation of thermal evolution curves of hybrid stars with deconfinement heating. Rise of surface temperature of stars is derived from the deconfinement heating. Rise of surface temperature accompany quark matter appearing It may be a evidence for existence of quark matter, if a heating period is observed for a very old pulsar.

Discussion The mass range of deconfined signal emerging can be changed with varying of some parameters(bag constant B, coupling constant g). The deconfinement heating rate is different for various stages of stars. This may lead to special effect of short timescale behaviors due to local heat deposit and enhanced neutrino emission. The details of evolution in years is worth discussion in future researches.

Different bag constant