Relativistic Force-Free Electrodynamic Simulations of Neutron Star Magnetospheres

The luminosity and structure of neutron star magnetospheres are crucial to our understanding of pulsar and plerion emission. A solution found using the force-free approximation would be an interesting standard with which any model with more physics could be compared. Prior quasi-analytic force-free solutions may not be stable, while prior time-dependent magnetohydrodynamic models used unphysical model parameters. We use a time-dependent relativistic force-free electrodynamics code with no free parameters to find a unique stationary solution for the axisymmetric rotating pulsar magnetosphere in a Minkowski space-time in the case of no surface currents on the star. The solution is similar to the force-free quasi-analytic solution of \citet{cont99} and the numerical magnetohydrodynamic solution of \citet{kom05}. The magnetosphere structure and the usefulness of the classical y-point in the general dissipative regime are discussed. The pulsar luminosity is found to be $L \approx 0.99\pm 0.01 \mu^2\Omega_\star^4/c^3$ for a dipole moment $\mu$ and stellar angular frequency $\Omega_\star$.