Finite force-free pulsar atmosphere models

Abstract

Models of cold plasma atmospheres in a dipole magnetic field which are both force-free, rho/sub q/(ExB)=0, and finite in extent are studied. These models satisfy the local force-free condition which is necessary for a minimum energy state and have the required continuous electric field at the plasma-vacuum surface. By Pilipp's theorem it is known that such atmospheres cannot rigidly rotate. The nature of this differential rotation of the plasma is determined for several models. It is noted that all finite models may allow for corotational, toroidal regions about the equatorial plane, characterized by the fact that these magnetic field lines do not extend into the vacuum region. For all models examined, the charge density has only one sign on all magnetic surfaces which extend into the vacuum. Since all models have an arbitrary scaling factor, any corotating portion of the magnetosphere may, or may not, have only one charge sign on magnetic surfaces. All models are apparently stable to guiding center perturbations, but obviously cannot all have the desired minimum configurational energy, which is one of the future refinements needed to select a realistic model. These models indicate that any current loop which might result from the cross-field breakdown ofmore » guiding center dynamics, due to E/sub perpendicular/>B, would occur near the juncture of the plasma-vacuum surface and the equatorial plane. Such currents would flow from a ring around the poles rather than directly from over the poles.« less