Rotating Magnetosphere: a Simple Relativistic Model

Abstract

We solve exactly for the electromagnetic field configuration about an aligned rotating magnetic moment ("star") for the case that there is sufficient plasma about the object to "freeze in" the magnetic fields, but in the limit that the inertia and pressure of the plasma particles can be neglected. These solutions are expected to be valid except near the light cylinder, although there is no mathematical difficulty in solving the resultant equations at or even beyond the light cylinder. The solutions show quantitatively how the field lines make the transition from a closed (dipole-like) to an open configuration and provide a refined estimate of how much magnetic flux is available to open field lines (an important point in many pulsar theories). We find that if a flux from an unperturbed dipole closes outside the light cylinder, then for the perturbed field this flux is increased by a factor of about 1.592. The field lines in the dipole case exhibit a cusp at the light cylinder, and we can calculate the charge density there. This charge density is found to be insufficient to account for coherent radiation of radiofrequency waves from pulsars. Subject headings: hydromagnetics - magnetic stars - pulsars - relativity - rotation, stellar