Time-dependent Force-free Pulsar Magnetospheres: Axisymmetric and Oblique Rotators

Magnetospheres of many astrophysical objects can be accurately described bythe low-inertia (or "force-free") limit of MHD. We present a new numericalmethod for solution of equations of force-free relativistic MHD based on thefinite-difference time-domain (FDTD) approach with a prescription for handlingspontaneous formation of current sheets. We use this method to study thetime-dependent evolution of pulsar magnetospheres in both aligned and obliquemagnetic geometries. For the aligned rotator we confirm the general propertiesof the time-independent solution of Contopoulos et al. (1999). For the obliquerotator we present the 3D structure of the magnetosphere and compute, for thefirst time, the spindown power of pulsars as a function of inclination of themagnetic axis. We find the pulsar spindown luminosity to be L = (mu^2Omega^4/c^3) (1+ sin^2(alpha)) for a star with the dipole moment "mu", rotationfrequency "Omega", and magnetic inclination angle "alpha". We also discuss theeffects of current sheet resistivity and reconnection on the structure andevolution of the magnetosphere.