Stability of Disk Galaxies in the Modified Dynamics

General analytic arguments lead us to expect that in the modified dynamics(MOND) self-gravitating disks are more stable than their like in Newtoniandynamics. We study this question numerically, using a particle-mesh code basedon a multi-grid solver for the (nonlinear) MOND field equation. We start withequilibrium distribution functions for MOND disk models having a smoothlytruncated, exponential surface-density profiles and a constant Toomre $Q$parameter. We find that, indeed, disks of a given ``temperature'' are locallymore stable in MOND than in Newtonian dynamics. As regards global instabilityto bar formation, we find that as the mean acceleration in the disk is lowered,the stability of the disk is increased as we cross from the Newtonian to theMOND regime. The degree of stability levels off deep in the MOND regime, asexpected from scaling laws in MOND. For the disk model we use, this maximumdegree of stability is similar to the one imparted to a Newtonian disk by ahalo three times as massive at five disk scale lengths.Comment: 20 pages, Latex, 8 embedded figures, version to be published in The Astrophys.