Partial Field Opening and Current Sheet Formation in the Disk Magnetosphere

In this paper I analyze the process of formation of thin current structures in the magnetosphere of a conducting accretion disk in response to the field-line twisting brought about by the rotation of the disk relative to the central star. I consider an axisymmetric force-free magnetically-linked star--disk configuration and investigate the expansion of the poloidal field lines and partial field-line opening caused by the differential rotation between the star and a nonuniformly-rotating disk. I present a simple analytical model that describes the asymptotic behavior of the field in the strong-expansion limit. I demonstrate the existence of a finite (of order one radian) critical twist angle, beyond which the poloidal field starts inflating very rapidly. If the relative star--disk twist is enhanced locally, in some finite part of the disk (which may be the case for a Keplerian disk that extends inward significantly closer to the central star than the corotation radius), then, as the twist is increased by a finite amount, the field approaches a partially-open configuration, with some field lines going out to infinity. Simultaneous with this partial field opening, a very thin, radially extended current layer forms, thus laying out a way towards reconnection in the disk magnetosphere. Reconnection, in turn, leads to a very interesting scenario for a quasi-periodic behavior of magnetically-linked star--disk systems with successive cycles of field inflation, opening, and reconnection.