Global static electrospheres of charged pulsars

Abstract

In this paper we present self-consistent models of the magnetosphere of inactive, charged, aligned rotator pulsars. We have devised an efficient semi-analytical and numerical algorithm to construct such models. The only free parameter is the total charge of the system. These charge-separated "electrospheres" consist of an equatorial belt carrying charge of one sign, partially in differential rotation, and of two oppositely charged domes located over the poles which corotate with the neutron star. The dependence of the shape of these plasma-filled regions surrounding the star on the total charge of the system and of their differential rotation is investigated. It is shown that our solutions are stable to vacuum breakdown by electron-positron pair production in most of the light-cylinder volume, except perhaps in the case of millisecond pulsars. The small regions where vacuum breakdown occurs are shown to behave merely as an effective extension of the star's volume. We have also found that no permanent null-charged wind emanating from the polar caps can exist in a stationary state. Indeed, for a given total charge of the system determined by the net outgoing charged flux, the potential configuration becomes unfavorable to particles escaping to infinity. Finally, we have shown that the geometric and kinematic structure of the electrosphere is uniquely determined by the total charge of the system.