Partial Field Opening and Current Sheet Formation in the Disk Magnetosphere

In this paper I analyze the process of formation of thin current structuresin the magnetosphere of a conducting accretion disk in response to thefield-line twisting brought about by the rotation of the disk relative to thecentral star. I consider an axisymmetric force-free magnetically-linkedstar--disk configuration and investigate the expansion of the poloidal fieldlines and partial field-line opening caused by the differential rotationbetween the star and a nonuniformly-rotating disk. I present a simpleanalytical model that describes the asymptotic behavior of the field in thestrong-expansion limit. I demonstrate the existence of a finite (of order oneradian) critical twist angle, beyond which the poloidal field starts inflatingvery rapidly. If the relative star--disk twist is enhanced locally, in somefinite part of the disk (which may be the case for a Keplerian disk thatextends inward significantly closer to the central star than the corotationradius), then, as the twist is increased by a finite amount, the fieldapproaches a partially-open configuration, with some field lines going out toinfinity. Simultaneous with this partial field opening, a very thin, radiallyextended current layer forms, thus laying out a way towards reconnection in thedisk magnetosphere. Reconnection, in turn, leads to a very interesting scenariofor a quasi-periodic behavior of magnetically-linked star--disk systems withsuccessive cycles of field inflation, opening, and reconnection.Comment: 27 pages, 7 figures; submitted to the Astrophysical Journa