Stellar Velocity Distribution in Galactic Disks
  We present numerical studies of the properties of the stellar velocity distribution in galactic disks which have developed a saturated, two-armed spiral structure. In previous papers we used the Boltzmann moment equations (BME) up to second order for our studies of the velocity structure in self-gravitating stellar disks. A key assumption of our BME approach is the zero-heat flux approximation, i.e. the neglection of third order velocity terms. We tested this assumption by performing test particle simulations for stars in a disk galaxy subject to a rotating spiral perturbation. As a result we corroborated qualitatively the complex velocity structure found in the BME approach. It turned out that an equilibrium configuration in velocity space is only slowly established on a typical timescale of 5 Gyrs or more. Since many dynamical processes in galaxies (like the growth of spirals or bars)act on shorter timescales, pure equilibrium models might not be fully appropriate for a detailed comparison with observations like the local Galactic velocity distribution. Third order velocity moments were typically small and uncorrelated over almost all of the disk with the exception of the 4:1 resonance region (UHR). Near the UHR (normalized) fourth and fifth order velocity moments are still of the same order as the second and third order terms. Thus, at the UHR higher order terms are not negligible. 
Christian Theis, Eduard Vorobyov