Stability of disk galaxies in the modified dynamics

General analytic arguments lead us to expect that in the modified Newtonian dynamics (MOND), self-gravitating disks are more stable than their like in Newtonian dynamics. We study this question numerically, using a particle-mesh code based on a multigrid solver for the (nonlinear) MOND field equation. We start with equilibrium distribution functions for MOND disk models having a smoothly truncated, exponential surface density profile and a constant Toomre Q-parameter. We find that, indeed, disks of a given "temperature" are locally more stable in MOND than in Newtonian dynamics. As regards global instability to 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 the MOND regime. The degree of stability levels off deep in the MOND regime, as expected from scaling laws in MOND. For the disk model we use, this maximum degree of stability is similar to the one imparted to a Newtonian disk. by a halo 3 times as massive at 5 disk scale lengths.