Abstract
Cold, magnetically supported, self-gravitating disks are evolutionary precursors of protostars. Magnetic tension balances self-gravity in these systems, so the magnetic field lines kink as they cross the disk. Previously, we have shown that such disks are marginally stable to in-plane perturbations. Here, we show that a sufficient condition for stability of such disks to out-of-plane, warping or tilting, perturbations is that the azimuthal current in the disk have one polarity as a function of radius. This corresponds to the gravitational acceleration in the disk pointing radially inward for all radii. This criterion is not necessary, however, and can be violated as long as the vertical magnetic field exceeds the radial magnetic field (in magnitude) everywhere in the disk.
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