Velocity distribution in stellar disks: Are higher order moments negligible?

Abstract

AbstractWe analysed the structure of the velocity space in galactic disks which are subject to a rotating spiral perturbation. A key assumption of the Boltzmann moment equation 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. The third order velocity moments were typically small (normalized values reach 25% of the initial velocity dispersion) and uncorrelated over almost all of the disk with the exception of the 4:1 resonance region (UHR). Even there, the values are smaller than the initial velocity dispersion. Far outside the resonance position a bimodal distribution characterizes the 3rd order moments. A qualitatively similar distribution is found for the 5th order terms. Contrary to these odd moments, the 4th order terms exceed almost everywhere the initial velocity dispersion. Therefore, an extension of the Boltzmann moment equations by only one moment, i.e. up to the third order, is not reasonable without including the fourth order terms. For all moments a large‐scale structure (either two‐armed or four‐armed) is clearly visible inside the UHR. The odd moments show a patchy irregular pattern outside the UHR, whereas the fourth order moments show also a clear large‐scale pattern. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)