Several glitches have been observed in young, isolated radio pulsars, while a clear detection in accretion-powered X-ray pulsars is still lacking. We use the Pizzochero snowplow model for pulsar glitches as well as starquake models to determine for the first time the expected properties of glitches in accreting pulsars and their observability. Since some accreting pulsars show accretion-induced long-term spin-up, we also investigate the possibility that anti-glitches occur in these stars. We find that glitches caused by quakes in a slow accreting neutron star are very rare and their detection extremely unlikely. On the contrary, glitches and anti-glitches caused by a transfer of angular momentum between the superfluid neutron vortices and the non-superfluid component may take place in accreting pulsars more often. We calculate the maximum jump in angular velocity of an anti-glitch and we find that it is expected to be about 1E-5 - 1E-4 rad/s. We also note that since accreting pulsars usually have rotational angular velocities lower than those of isolated glitching pulsars, both glitches and anti-glitches are expected to have long rise and recovery timescales compared to isolated glitching pulsars, with glitches and anti-glitches appearing as a simple step in angular velocity. Among accreting pulsars, we find that GX 1+4 is the best candidate for the detection of glitches with currently operating X-ray instruments and future missions such as the proposed Large Observatory for X-ray Timing (LOFT).
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