Measuring glitch recoveries and braking indices with Bayesian model selection

Abstract

ABSTRACT For a selection of 35 pulsars with large spin-up glitches ($\Delta {\nu }/\nu \ge 10^{-6}$), which are monitored by the Jodrell Bank Observatory, we analyse 157 glitches and their recoveries. All parameters are measured consistently and we choose the best model to describe the post-glitch recovery based on Bayesian evidence. We present updated glitch epochs, sizes, changes of spin down rate, exponentially recovering components (amplitude and corresponding time-scale) when present, as well as pulsars’ second frequency derivatives and their glitch-associated changes if detected. We discuss the different observed styles of post-glitch recovery as well as some particularly interesting sources. Several correlations are revealed between glitch parameters and pulsar spin parameters, including a very strong correlation between a pulsar’s interglitch $|\ddot{\nu }|$ and $\dot{\nu }$, as well as between the glitch-induced spin-down rate change $\Delta \dot{\nu }_{\rm p}$ that does not relax exponentially and $\dot{\nu }$. We find that the ratio $\left|\Delta \dot{\nu }_{\mathrm{p}}/\ddot{\nu }\right|$ can be used as an estimate of glitch recurrence times, especially for those pulsars for which there are indications of a characteristic glitch size and interglitch waiting time. We calculate the interglitch braking index n and find that pulsars with large glitches typically have n greater than 3, suggesting that internal torques dominate the rotational evolution between glitches. The external torque, for example, from electromagnetic dipole radiation, could dominate the observed $\ddot{\nu }$ for the youngest pulsars ($\lesssim 10^{4}\,\,\mathrm{yr}$), which may be expected to display $n\sim 3$.