Bayesian Insights into post-Glitch Dynamics: Model comparison and parameter constraint from decades long observation data of the Crab pulsar

The Crab Pulsar has exhibited numerous glitches accompanied by persistent shifts in its spin-down rate. The explanation of the observed persistent shifts remain a challenge. We perform a detailed Bayesian analysis to compare four data-fitting models, ranging from a simple linear model to more complex power-law and logarithmic models, using a dataset of observed glitches and persistent shifts. Our results show the large observed events are difficult to explain by the usually assumed linear model due to starquakes. A particularly notable finding is that the logarithmic model provides the best fit to the observation data but the two power-law models show a close tie to it. Detail differences of these models may be further clarified by the understanding of internal physics of neutron stars.