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. Subject headings: accretion, accretion disks — magnetic fields — MHD — stars: magnetic fields