On the overall properties of young neutron stars: an application to the Crab pulsar

In this brief report, we present a model that complements the well-established canonical model for the spin evolution of rotation-powered pulsars, which is typically used to estimate ages, spin-down luminosity, and surface magnetic fields of middle-aged pulsars. We analytically explore the growth of the magnetic field during a pulsar’s early history, a period shortly after supernova explosion from which the neutron star forms, encompassing the hypercritical phase and subsequent reemergence of the magnetic field. We analyze the impact of such growth on the early dynamics of the pulsar. Investigations into a pulsar’s magnetic evolution are not new, and we expand the knowledge in this area by examining the evolutionary implications in a scenario governed by growth functions. The proposed growth functions, calibrated with data from the Crab pulsar, exhibit satisfactory physical behaviors.