Statistics of neutron stars at the stage of a supersonic propeller

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Abstract
We analyze the statistical distribution of neutron stars at the stage of a supersonic propeller. An important point of our analysis is allowance for the evolution of the angle of inclination of the magnetic axis to the spin axis of the neutron star for the boundary of the transition to the supersonic propeller stage. We have determined the spin period distributions of pulsars at the propeller stage for two models: the model with hindered particle escape from the stellar surface and the model with free particle escape. As a result, we have shown that consistent allowance for the evolution of the inclination angle in the region of extinct radio pulsars for the two models leads to an increase in the total number of neutron stars at the supersonic propeller stage. This increase stems from the fact that when allowing for the evolution of the inclination angle χ for neutron stars in the region of extinct radio pulsars and, hence, for the boundary of the transition to the propeller stage, this transition is possible at shorter spin periods (P ∼ 5–10 s) than assumed in the standard model.

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