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 unrecovered, long-term increase in the magnitude of its spindown rate (|ν ̇|) 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 the Jodrell Bank Crabglitch timing archive up to 2017 glitch of crab pulsar. Our results show the large observed events (Δν > 5 μHz) are difficult to explain by the usually assumed linear model due to starquakes. A particularly notable finding is that the logarithmic model, may arise from a cascading magnetospheric readjustment in which the openflux fraction changes as logarithmic form or some internal mechanism, provides the best fit, although two powerlaw alternatives trail closely. These nonlinear models may have been clarified by understanding the internal physics of neutron stars.