The interaction of a stellar magnetosphere with a thin accretion disk
is considered. Specifically, I consider a model in which (1) the accre
tion disk is magnetically linked to the star over a large range of rad
ii and (2) the magnetic diffusivity of the disk is sufficiently small
that there is little slippage of field lines within the disk on the ro
tation time scale. In this case the magnetic energy built up as a resu
lt of differential rotation between the star and the disk is released
in quasi-periodic reconnection events occuring in the magnetosphere (A
ly and Kuijpers 1990). The radial transport of magnetic flux in such a
n accretion disk is considered. It is show that the magnetic flux dist
ribution is stationary on the accretion time scale, provided the time
average of the radial component of the field just above the disk vanis
hes. A simple model of the time-dependent structure of the magnetosphe
re is presented. It is shown that energy release in the magnetosphere
must take place for (differential) rotation angles less than about 3 r
adians. The magnetic flux distribution in the disk depends on the prec
ise value of the rotation angle.