The dynamics of pulsar glitches: Contrasting phenomenology with numerical evolutions

In this paper we consider a simple two-fluid model for pulsar glitches. We derive the basic equations that govern the spin evolution of the system from two-fluid hydrodynamics, accounting for the vortex mediated mutual friction force that determines the glitch rise. This leads to a simple "bulk" model that can be used to describe the main properties of a glitch event resulting from vortex unpinning. In order to model the long term relaxation following the glitch our model would require additional assumptions regarding the repinning of vortices, an issue that we only touch upon briefly. Instead, we focus on comparing the phenomenological model to results obtained from time-evolutions of the linearised two-fluid equations, i.e. a "hydrodynamic" model for glitches. This allows us to study, for the first time, dynamics that was "averaged" in the bulk model, i.e. consider the various neutron star oscillation modes that are excited during a glitch. The hydro-results are of some relevance for efforts to detect gravitational waves from glitching pulsars, although the conclusions drawn from our rather simple model are pessimistic as far as the detectability of these events is concerned.