Electrodynamics of axisymmetric pulsar magnetosphere with electron-positron discharge: a numerical experiment

Abstract

We present the first self-consistent global simulations of pulsar magnetospheres with operating $e^\pm$ discharge. We focus on the simple configuration of an aligned or anti-aligned rotator. The star is spun up from zero (vacuum) state to a high angular velocity, and we follow the coupled evolution of its external electromagnetic field and plasma particles using the "particle-in-cell" method. A plasma magnetosphere begins to form through the extraction of particles from the star; these particles are accelerated by the rotation-induced electric field, producing curvature radiation and igniting $e^\pm$ discharge. We follow the system evolution for several revolution periods, longer than required to reach a quasi-steady state. Our numerical experiment puts to test previous ideas for the plasma flow and gaps in the pulsar magnetosphere. We first consider rotators capable of producing pairs out to the light cylinder through photon-photon collisions. We find that their magnetospheres are similar to the previously obtained force-free solutions with a current sheet and the Y-point near the light cylinder. The magnetosphere continually ejects $e^\pm$ pairs and ions. Pair creation is sustained by a strong electric field along the current sheet. We observe powerful curvature and synchrotron emission from the current sheet, consistent with Fermi observations of gamma-ray pulsars. We then study pulsars that can only create pairs in the strong-field region near the neutron star, well inside the light cylinder. We find that both aligned and anti-aligned rotators relax to the "dead" state with suppressed pair creation and electric currents, regardless of the discharge voltage.