Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Compressive tidal heating of a disk galaxy in a rich cluster

The restricted three-body method is used to model the effect of the mean tidal field of a cluster of galaxies on the internal dynamics of a disk galaxy falling into the cluster for the first time. In the model adopted the galaxy experiences a tidal field that is compressive within the core of the cluster. The planar random velocities of all components in the disk increase after the galaxy passes through the core of the cluster. The low-velocity dispersion gas clouds experience a relatively larger increase in random velocity than the hotter stellar components. The increase in planar velocities results in a strong anisotropy between the planar and vertical velocity dispersions. It is argued that this will make the disk unstable to the 'fire-hose instability' which leads to bending modes in the disk and which will thicken the disk slightly. The mean tidal fields in rich clusters were probably stronger during the epoch of cluster formation and relaxation than they are in present-day relaxed clusters.