Pulsar magnetospheres with arbitrary geometry in the force-free approximation

Abstract

Some general properties are derived of force-free configurations describing pulsar magnetospheres in the wave-zone, well beyond the light cylinder. No restrictions are imposed on geometry, or on the ‘parallel current function’ ψ. The work is confined to solutions free of magnetic monopoles, and possessing finite flux of energy to infinity. It is found that application of the obvious inertial constraint υ ≤ c removes a considerable part of the arbitrariness inherent in the force-free approximation. All solutions then have the following properties, (a) They possess magnetic neutral sheets, (b) The far field takes the form of an outwardly propagating vacuum wave (a radiation condition having removed the inwardly propagating solutions), (c) All charged particle speeds approach c at large distances, in such a way that their Lorentz factors increase roughly linearly with distance, (d) There always exist zones where counterstreaming of charged particles occurs (while their speeds are appreciably less than c). Some of these properties bring into question the validity of the force-free approximation.