Simulations of the axisymmetric magnetospheres of neutron stars

In this paper we present the results of time-dependent simulations of the dipolar axisymmetric magnetospheres of neutron stars carried out within the frameworks of both relativistic magnetohydrodynamics (MHD) and resistive force-free electrodynamics. The results of force-free simulations reveal the inability of our numerical method to accommodate the equatorial current sheets of pulsar magnetospheres, and raise a question mark about the robustness of this approach. On the other hand, the MHD approach allows us to make significant progress. We start with a non-rotating magnetically dominated dipolar magnetosphere and follow its evolution as the stellar rotation is switched on. We find that the time-dependent solution gradually approaches a steady state that is very close to the stationary solution of the pulsar equation found in 1999 by Contopoulos, Kazanas & Fendt. This result suggests that other stationary solutions that have the Y-point located well inside the light cylinder are unstable. The role of particle inertia and pressure on the structure and dynamics of MHD magnetospheres is studied in detail, as well as the potential implications of dissipative processes in the equatorial current sheet. We argue that pulsars may have differentially rotating magnetospheres which develop noticeable structural oscillations, and that this may help to explain the nature of the subpulse phenomena.