On Nonshearing Magnetic Configurations in Differentially Rotating Disks

A new class of disk MHD equilibrium solutions is described, which is valid within the standard local (``shearing sheet'') approximation scheme. These solutions have the following remarkable property: velocity streamlines and magnetic lines of force rotate rigidly, even in the presence of differential rotation. This situation comes about because the Lorentz forces acting upon modified epicycles compel fluid elements to follow magnetic lines of force. Field line (and streamline) configurations may be elliptical or hyperbolic, prograde or retrograde. These structures have previously known hydrodynamical analogs: the ``planet'' solutions described by Goodman, Narayan, & Goldreich. The primary focus of this investigation is configurations in the disk plane. A related family of solutions lying in a vertical plane is briefly discussed; other families of solutions may exist. Whether these MHD structures are stable is not yet known, but could readily be determined by three-dimensional simulations. If stable or quasi-stable, these simple structures may find important applications in both accretion and galactic disks.