Potential-density pairs for flat discs

Abstract

We simplify Lynden-Bell's (1989) extension to non-axisymmetric disks of Mestel's (1963) method of flattened spheroids for finding potential–density pairs is simplified. It is used to find a large family of potential–density pairs, which is described by a pair of generalized hypergeometric functions. A portion of this family is explored; some new pairs are found, and many already known ones are recovered. Among the new pairs found are ones related to non-axisymmetric distortions of the Kuzmin–Toomre, Gaussian, Kalnajs–Mestel, and isochrone disks, and which should be useful for stability analyses of these disks.