Prediction of Pulsar Glitch Frequency Based on the Hard Superfluid Model

Abstract

Observations of the discontinuities in the pulsar rotation periods (glitches) provide us with a unique probe into the neutron star structure. In recent years a great deal of effort has been devoted to the better under· standing of the glitch phenomena in the framework of the model. 1)-6) This model relates the glitches with the unpinning of the neutron vortex lines in the inner crust of a neutron star. The vortex lines of the neutron are usually pinned to the nuclei at the lattice sites; hence the term hard superiluid was coined on the analogy of supercon· ductors. In a recent paper Backus, Taylor and Damashek ) reported a discovery of a superglitch in the pulsar PSRZZZ4+65 combining with the measurements of Helfand et a1. ) It is the purpose of this letter to analyze the superglitch frequency based on the superfiuid model and predict forthcoming superglitches. In this letter we work in the simplest ver· sion of the superfluid model. Immedi· ately after a glitch the neutron superfiuid in the inner crust of a neutron star is supposed to be rotating synchronously with the crust. As time passes the crust is decelerated owing to the slowing down of the pulsar. The neutron cannot follow the deceleration of the crust, since the vortex lines are tightly pinned to the crustal nuclei and the areal number density of vortex lines cannot change. Thus the relative velocity between the neutron and the crustal lattice increases with time. When the Magnus force due to the velocity difference surpasses the smaller of the pinning force and the lattice fracture force, the superfluous vortex lines start moving outward, and the excess angular momentum is transferred from the neutron to the crust. The crust is thus spun up. This is the next glitch of the pulsar. As a matter of fact the condition stated in the above corresponds to the local unpinning of the vortex lines. In order to obtain a macroscopic glitch we have to have a global unpinning of the vortex lines. In other words some collective mechanism must work in order to bring about a sufficient amount of unpinning of the vortex lines to cause a stellar phenomenon. A mechanism involving the boundary layer has been proposed by Alpar, et a1. ) Although the collective mechanism has not been worked out completely so far, we shall assume an enhancement of the Magnus force by some collective mechanism. Thus the glitch condition is written as