Bayesian estimate of the superfluid moments of inertia from the 2016 glitch in the Vela pulsar

Abstract

Context. The observation of the first pulse-to-pulse glitch in the Vela pulsar opens a new window among theoretical speculations on the internal dynamics of neutron stars as it allows us for testing models to factor in the circumstances of the first moments of a glitch. Several works in the literature have already considered the observational and physical parameters of the star by employing a minimal model with three rigidly rotating components. Aims. We improve the analytical study of the minimal three-component model for pulsar glitches by solving it with generic initial conditions for the two initial lags of their superfluid components. The purpose is to use this solution to fit the data of the 2016 Vela glitch by employing a Bayesian approach and to obtain a probability distribution for the physical parameters of the model and for observational parameters, such as the glitch rise time and the relaxation timescale. Methods. The fit is achieved through Bayesian inference. Due to the presence of an increase in the timing residuals near the glitch time, an extra magnetospheric component was added to the three-component model to deal with this phenomenon. A physically reasonable, non-informative prior was set on the different parameters of the model, so that the posterior distribution could be compared with state-of-the-art information obtained from microphysical calculations. By considering a model with a tightened prior on the moment of inertia fractions and by comparing it with the original model by means of Bayesian model selection, we studied the possibility of a crust-limited superfluid reservoir. Results. We obtained the posterior distribution for the moment of inertia fractions of the superfluid components, the coupling parameters, and the initial velocity lags between the components. An analysis of the inferred posterior also confirmed the presence of an overshoot in that glitch and set an upper limit of ∼6 s on the glitch rise timescale. The comparison between the two models with different priors on the moment of inertia fractions appears to indicate a need for a core participation in the glitch phenomenon, regardless of the uncertain strength of the entrainment coupling.