THE STABILITY OF COLD, FLATTENED, SELF-GRAVITATING DISKS OBEYING OTHER THAN NEWTONIAN FORCE LAWS

Three proposed non-Newtonian dynamical theories seem to explain "naturally" the flat rotation curves of spiral galaxies without assuming the existence of a massive but nonluminous "dark halo" component surrounding the disks of these galaxies. Apart from the two already well-known theories of modified gravity advanced by Milgrom and Tohline, Mannheim and Kazanas in 1989 have discovered yet another theory that strives to explain the dynamics of galaxies and clusters of galaxies as simply due to the existence of a long-range, constant-magnitude force. Assuming, however, that such forces may really exist, we have to examine the fundamental problem of the stability of self-gravitating, cold (rapidly rotating) disks to nonaxisymmetric perturbations. We have used an "N-body" computer code to perform a stability analysis of all the above theories. Our results agree with previous studies of cold, self-gravitating disks with Newtonian and 1/r force laws (unstable to a barlike distortion and stable, respectively). In addition, we find that disks with a long-range force of constant magnitude are also stable and, in agreement with the prediction of Milgrom in 1989, that disks under the action of a force law of the modified Newtonian dynamics type make the transition to stability as the MOND force begins to dominate everywhere over the purely Newtonian force. Apparently, the present results cannot be used either in favor or against any of the proposed theories of modified gravity.