The Spin Period, Luminosity, and Age Distributions of Anomalous X‐Ray Pulsars

We consider the accretion model for anomalous X-ray pulsars proposed recentlyby Chatterjee, Hernquist and Narayan, in which the emission is powered byaccretion from a fossil disk formed by the fallback of material from asupernova explosion. We demonstrate that this model is able to account for thespin period, luminosity and age distributions of the observed population ofAXPs for reasonable and broad distributions of the free parameters of themodel, namely, the surface magnetic field of the neutron star, the mass of itsaccretion disk and its initial spin period. In particular, this model is ablestatistically to account for the puzzlingly narrow observed spin distributionof the AXPs. We show also that if the establishment of fallback accretion disksaround isolated neutron stars is a universal phenomenon, then a fairly largeminority ($\sim 20%$) of these objects become X-ray bright AXPs or X-ray faintsystems spinning down by propeller action, while the rest become radio pulsars.Comment: 11 pages, 2 figures; accepted for publication in Ap