Relating Braking Indices of Young Pulsars to the Dynamics of Superfluid Cores

Abstract

Pulsars are stars that emit electromagnetic radiation in well-defined time intervals. The frequency of such pulses decays with time as is quantified by the {\it braking index} ($n$). In the canonical model $n = 3$ for all pulsars, but observational data show that $n \neq 3$, indicating a limitation of the model. In this work we present a new approach to study the frequency decay of the rotation of a pulsar, based on an adaptation of the canonical one. We consider the pulsar a star that rotates in vacuum and has a strong magnetic field but, differently from the canonical model, we assume that its moment of inertia changes in time due to a uniform variation of a displacement parameter in time. We found that the braking index results smaller than the canonical value as a consequence of an increase in the star's displacement parameter, whose variation is small enough to allow plausible physical considerations that can be applied to a more complex model for pulsars in the future. In particular, this variation is of the order of neutron vortices' creep in rotating superfluids. When applied to pulsar data our model yielded values for the stars' braking indices close to the observational ones. The application of this approach to a more complex star model, where pulsars are assumed to have superfluid interiors, is the next step in probing it. We hypothesize that the slow expansion of the displacement parameter might mimic the motion of core superfluid neutron vortices in realistic models.