Stellar distribution functions for galactic disks

The phase-space distribution function for an axisymmetric stellar galactic disk is determined in terms of three particular integrals of motion. The three action integrals are calculated for individual stellar orbits using spectral stellar dynamics techniques. A set of 2000 orbits resulting from numerical simulations of the heating of an initially cold stellar population by giant molecular clouds is computed. The distribution function is well approximated by products of exponentials of the two actions J(R) and J(theta) associated with the radial and vertical motion and a function of the azimuthal angular momentum. The action integrals J(R) and J(theta) are uncorrelated, so the amplitudes of the radial and vertical motions of the stars are decoupled. The epicyclic approximation is satisfied for the majority of the orbits studied, and in this approximation exponential dependence of f on J(R) and J(theta) implies that the random velocities in the disk have Maxwellian distributions.