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An expression is derived for changes induced in the phase-space distribution function when a galactic disk's dynamical structure is changed by fluctuations in its gravitational potential field. The changes are found to be second-order in the perturbing potential, and of the form of a diffusion in phase space. This result is evaluated for the case of a model transient spiral. The radial velocity dispersion of the stars increases in response to a steady sequence of perturbations as t to the 1/2-power for low velocity stars, declining to t to the 1/5-power as the radial excursions of stars become large by comparison with the spirals' spatial wavelength. The present predictions are in agreement with the age/velocity dispersion relation observed in N-body experiments. It is concluded that recurrent transient spirals naturally account for the velocity-dispersion relation observed for the solar neighborhood stars.
Carlberg et al. (Wed,) studied this question.