A MODEL FOR THE VERTICAL-DISTRIBUTION OF STARS IN DISK GALAXIES

We investigate the contribution of multiple velocity dispersion components to the vertical (z) distribution of stars in a disk galaxy by self-consistently solving the Poisson and collisionless Botzmann equations. To reduce significantly the number of free parameters, we incorporate a history of galaxian star formation which produces stellar populations with evolving velocity dispersions. This also allows us to evaluate contributions to the width of the disk from different epochs of stellar creation. In general, our predicted vertical brightness dis tribution is thinner than a ''standard'' isothermal sech2 (z) function if the latter is fitted to the high-z wings of the density distribution, as additional stellar components in our model have smaller vertical velocity dispersions than the dominant, high-z one. Alternatively, if a sech2 (z) function is used to approximate our model at intermediate vertical heights, as is usually the case in fitting observational data, at large z we predict a modest excess of stars above that of the analytic function. This may be analogous to the ''thick disk'' reported by some workers. However, it is very difficult to distinguish observationally between otherwise very dissimilar models: typical differences between a single-component isothermal system and our multicomponent models are less than 1%. We also evaluate the effects of a hypothetical dark matter halo. With typical published data, dark matter cannot be unambiguously distinguished by its effect on vertical brightness distributions: modest variations in nondark matter parameters can approximate the effects of dark matter. However, with dark matter our models predict distinctive behavior of stellar densities far from the galactic plane, which may be detected with very high quality data.