Dynamical evolution in galactic disks

Abstract

The dynamical structure of a galactic disk is changed by fluctuations in its gravitational potential field. The orbits of stars are deflected, changing the velocity dispersion and angular-momentum distribution. We derive an expression for the induced changes in the phase-space distribution function, finding them to be second order in the perturbing potential, and of the form of a diffusion in phase space. We evaluate our result for a model transient spiral. The radial-velocity dispersion of the stars increases in response to a steady sequence of perturbations as t/sup 1/2/, for low velocity stars, declining towards t/sup 1/5/ as the radial excursions of stars become large in comparison to the spatial wavelength of the spirals. The waves also transport angular momentum, allowing the disk to become more centrally concentrated. In equilibrium the wave amplitude is controlled by the rate of dynamical cooling in the disk, and, inasmuch as the gas also gives rise to star formation, the heating time scale may be similar to the galactic star-formation time scale. Spiral waves may then rearrange the structure of the disk, as stars form out of the gas. Our predictions are in good agreement with the age/velocity-dispersion relation observed in our N-body experiments,more » and we conclude that recurrent transient spirals naturally account for that observed for the solar neighborhood stars.« less