Accretion magnetospheres: General solutions

The problem of finding the equilibrium magnetopause shape around a dipole-magnetized star, where that magnetic field is confined by external plasma, is reduced to that of solving an integral equation. The resultant equation can be efficiently solved numerically, and comparison is given for several previously considered models of the external plasma pressure. Also, analytic solutions are possible, and one is derived for the transition case P=r-6, wherein the magnetopause shape is given by r=sin theta, supporting the conjecture that no detached magnetosphere exists in this case (i.e., one surrounding but not reaching the dipole-field source). Axial symmetry is assumed in the derivation of the integral equation, but symmetry about the equator is not. Moreover, source fields more complex than the pure dipole can in principle be treated