Force-Free Electrodynamics of Pulsars

Abstract

We show that FFE (Force-Free Electrodynamics) describes pulsar magnetospheres -- even when radiation and particle wind power are comparable to the spin-down power. At the same time, we show that FFE is insufficient for calculating pulsar magnetospheres. This is because FFE admits a large family of stationary solutions with different currents flowing in the closed line region. To choose the actual solution one needs a model of current generation which goes beyond pure FFE. We calculate several FFE magnetospheres for the aligned rotator. The Poynting power of these solutions fills the range $c^{-3}μ^2Ω^4~< ~L~ <~ 0.67 c^{-3}μ^2Ω^4(c/ΩR_s)^2$, for angular velocity $Ω$ and magnetic field which is a pure dipole $μ$ on the surface of the star of radius $R_s$. Anomalous braking indices of young pulsars might be explained by currents flowing in the closed-line region.