Rotational evolution of the Crab pulsar in the wind braking model

Abstract

The pulsar wind model is updated by considering the effect of particle density and pulsar death. It can describe both the short-term and long-term rotational evolution of pulsars consistently. It is applied to model the rotational evolution of the Crab pulsar. The pulsar is spun down by a combination of magnetic dipole radiation and particle wind. The parameters of the Crab pulsar, including magnetic field, inclination angle, and particle density are calculated. The primary particle density in acceleration region is about 103 times the Goldreich-Julian charge density. The lower braking index between glitches is due to a larger outflowing particle density. This may be glitch induced magnetospheric activities in normal pulsars. Evolution of braking index and the Crab pulsar in P - P diagram are calculated. The Crab pulsar will evolve from magnetic dipole radiation dominated case towards particle wind-dominated case. Considering the effect of pulsar 'death', the Crab pulsar (and other normal pulsars) will not evolve to the cluster of magnetars but downwards to the death valley. Different acceleration models are also considered. Applications to other sources are also discussed, including pulsars with braking index measured, and the magnetar population.