Energy release in stellar magnetospheres

The interaction of a stellar magnetosphere with a thin accretion disk is considered. Specifically, I consider a model in which (1) the accretion disk is magnetically linked to the star over a large range of radii and (2) the magnetic diffusivity of the disk is sufficiently small that there is little slippage of field lines within the disk on the rotation time scale. In this case the magnetic energy built up as a result of differential rotation between the star and the disk is released in quasi-periodic reconnection events occuring in the magnetosphere (Aly and Kuijpers 1990). The radial transport of magnetic flux in such an accretion disk is considered. It is show that the magnetic flux distribution is stationary on the accretion time scale, provided the time average of the radial component of the field just above the disk vanishes. A simple model of the time-dependent structure of the magnetosphere is presented. It is shown that energy release in the magnetosphere must take place for (differential) rotation angles less than about 3 radians. The magnetic flux distribution in the disk depends on the precise value of the rotation angle.