The influence of massive gas clouds on stellar velocity dispersions in galactic discs

This paper calculates the evolution of the three components of the velocity dispersion of the stars in a galactic disc due to the influence of massive gas clouds in circular orbits in the disc. We find that there are two phases in this evolution: an initial transient phase in which the shape of the velocity ellipsoid relaxes to a final shape depending only on the ratio $$\Omega/\kappa$$ of the circular to the radial epicyclic frequencies, followed by a steady heating phase in which for typical disc stars the velocity dispersion σ varies as $$d\sigma^2/dt\propto N_\text cM^2_\text c\nu/\sigma^2$$, where N_c and M_c are the surface density and mass of the clouds and ν is the vertical epicyclic frequency. We also find that the amount of stellar heating predicted will be comparable with that observed, for young stars at least, if cloud masses are near the upper end of the observationally allowed range, but that the ratio of vertical to horizontal velocity dispersions predicted disagrees with that observed. This may indicate that other disc heating mechanisms are important.