COOLING AND SPIN-DOWN OF PULSARS WITH EVOLVING ROTATING EQUILIBRIUM CONFIGURATION .2. EFFECTS OF EQUATIONS OF STATE

We assume that an evolving rotating pulsar can be approximated by an equilibrium configuration of Maclaurin spheroid whose gravitational and rotational energies can be uniquely specified by stellar angular velocity OMEGA. Two heating mechanisms, namely the vortex creeping process and the crust-cracking process, are included in the evolution model. Various equations of state are used to construct stellar models, and therefore effects of stellar model on the cooling and spin-down of pulsars in such evolving rotating equilibrium configuration can be found. We show that the physical quantities of a pulsar, such as stellar radius, mass of crust region, surface gravity, density, and strength of crust, which are sensitive to the equation of state chosen for given mass and surface magnetic field, significantly affect the cooling and spin-down of pulsars with heating mechanisms. Exotic cooling processes, such as direct Urca neutrino emission process and pion condensation neutrino emission, are included in our calculation for specified stellar model. The heating mechanisms-the crust cracking and vortex creeping processes-are appreciably stronger in the stiffer star than in the softer one. In this paper, the observed data of pulsars, PSR 0531 + 21, PSR 0833 - 45, PSR 0656 + 14, PSR 1055 - 52, PSR 1929 + 10, and Geminga, are employed to put constraints on the heating parameters. Our results indicate that these constraints favors the pulsars to have stiff equation of state than soft one if heating mechanisms do exist.