Stochastic processes in a multi-component pulsar model

Abstract

Timing noise or spin wandering is a steady, long-term, observable, stochastic fluctuation in the rotational frequency of pulsars. It is a process believed to be a manifestation of dynamics intrinsic to the pulsar itself. In this work, we adopt a generic stochastic multi-component pulsar model describing the spin down evolution of a neutron star, which incorporates the coupling effect between a rotating normal component and a superfluid component. We generate simulated angular velocity residuals for both components using the Euler-Maruyama scheme then compute the empirical mean-square deviations (MSDs) for different models, representing low/high coupling and normal/superfluid component dominated inertia. We also calculate the theoretically expected MSDs from an exact expression derived for the underlying stochastic model. We compare the empirical MSDs derived from the simulated timeseries with their corresponding theoretical MSDs to check for consistency. We find that while in some cases, the theoretical and empirical MSDs are consistent, in general, they only match for certain ranges of lag time. While pinpointing the source of the discrepancy is outside the scope of this work, our results indicate the need to revisit reported results based on this methodology and further work to devise alternate schemes for improved modeling of pulsar timing noise from stochastic models.