ECCENTRIC BEHAVIOR OF DISK GALAXIES

摘要

A theory is developed for the dynamics of eccentric perturbations of a disk galaxy residing in a spherical dark matter halo and including a spherical bulge component. The disk is rep- resented as a large number N of rings with shifted centers and with perturbed azimuthal matter distribu- tions. Account is taken of the dynamics of the shift of the matter at the galaxy's center which may include a massive black hole. The gravitational interactions between the rings and between the rings and the center is fully accounted for, but the halo and bulge components are treated as passive gravitational field sources. Equations of motion and a Lagrangian are derived for the ring + center system, and these lead to total energy and total angular momentum constants of the motion. We first study the eccentric motion of a disk consisting of two rings of different radii but equal mass, Md/2, For small Ma the two rings are stable, but for Ma larger than a threshold value the rings are unstable with a dynamical timescale growth. For Ma sufficiently above this threshold, the instability acts to decrease the angular momentum of the inner ring, while increasing that of the outer ring. The insta- bility results from the merging positive and negative energy modes with increasing Md Second, we analyze the eccentric motion of one ring interacting with a radially shifted central mass. In this case instability sets in above a threshold value of the central mass (for a fixed ring mass), and it acts to increase the angular momentum of the central mass (which therefore rotates in the direction of the di