Effects of evolving rotating equilibrium configurations on the cooling and spin-down of pulsars

Abstract

We model a pulsar by a uniform density rotating spheroid covered by a solid crust. During the spin-down (up) epoch, pulsars can adjust their shapes to their equilibrium configurations, which depend on the stellar rotation velocity Ω, due to plastic flow and continuous crust breaking resulting from various mechanisms even though the crust is supposedly rigid. We show that this results in a coupling among the stellar temperature (T). the rotation velocity (Ω) and the eccentricity (e). and cooling and spin-down therefore mutually affect each other. Theoretically, crust cracking could be the dominant heating mechanism for pulsars instead of the vortex creeping mechanism if the crust is an ideal Coulomb lattice. But the present observed X-ray data can only provide constraints on the parameters of these two heating mechanisms and cannot determine which is the dominant one. For weak field millisecond pulsars, either one can lead to heating balancing the blackbody cooling, thus making these pulsars persistent soft X-ray emitters. Other implications and observational consequences of these heating mechanisms are discussed in the text.