The Power of Axisymmetric Pulsar

Abstract

Stationary force-free magnetosphere of an axisymmetric pulsar is shown to have a separatrix inclination angle of 77.3$^\circ$. The electromagnetic field has an $R^{-1/2}$ singularity inside the separatrix near the light cylinder. A numerical simulation of the magnetosphere which crudely reproduces these properties is presented. The numerical results are used to estimate the power of an axisymmetric pulsar: $L=(1\pm 0.1)\mu^2\Omega^4/c^3$. A need for a better numerical simulation is pointed out.