Velocity distribution of stars and relaxation in the galactic disk

Wielen (1977) has found that the observed increase of the velocity dispersion of disk stars with increasing age indicates strongly a significant irregular gravitational field in the galactic disk. This irregular field causes a rapid diffusion of stellar orbits in velocity and positional space. The effect of the irregular gravitational field on stellar orbits can be described quantitatively by a diffusion coefficient in velocity space. The diffusion coefficient may depend on the velocity of a star, on time, and on position. In the present investigation, some typical cases are discussed, taking into account the constant diffusion coefficient, a velocity-dependent coefficient, and a velocity-time-dependent coefficient. The theory of the diffusion of stellar orbits is found to predict successfully the observed velocity distribution of nearby disk stars. Attention is given to the implications for the vertical scale height of galactic disks.