Statistics of extinct radio pulsars

Abstract

We study the statistical distribution of extinct radio pulsars -- isolated neutron stars, that just crossed the death line. An important element that distinguishes our study from other works is a consistent allowance for the evolution of the angle between the magnetic and spin axes. We find the distribution of extinct radio pulsars in spin period for two models: the model with hindered particle escape from the neutron star surface and the model with free particle escape. The total number of extinct radio pulsars is shown to be much smaller than for the model in which the evolution of an inclination angle is disregarded. The decrease in total number of extinct radio pulsars arises from the fact, that account for evolution of the inclination angle allows the transition of a neutron star to the propeller stage appear at much smaller periods (P~5-10 s) than it is commonly assumed.