EQUILIBRIA OF FLAT AND ROUND GALACTIC DISCS

A general method is presented for constructing distribution functions for flat systems whose surface density and Toomre Q number profile are given. The purpose of these functions is to provide plausible galacti c models and assess their critical stability with respect to global no n-axisymmetric modes. The derivation may be carried out for an azimuth al velocity distribution (or a given specific energy distribution) whi ch may either be observed or be chosen to match a specified temperatur e profile. Distribution functions describing stable models with realis tic velocity distributions for power-law discs, the isochrone and the Kuzmin discs are provided. Specially simple inversion formulae are als o given for finding distribution functions for flat systems the surfac e densities of which are known.