Eccentric instability of a two-dimensional fluid disc with a central massive object

Abstract

In this paper we investigate, by linear modal analysis, the one‐armed dynamical instability of a two‐dimensional fluid disc that has a massive object at its centre. The model of the disc is chosen to avoid the artificial instabilities that originate from the unrealistic disc configurations that have been adopted in previous studies. We find a one‐armed instability for which the central massive object is displaced from the centre, which is generally called the ‘eccentric instability’. However, to excite the eccentric instability, the mass of the central object should be appreciably smaller than that of the disc, and this mass ratio is far smaller than what was originally proposed. The instability shown in this paper is likely to be excited in a stellar system with a central massive object, e.g. a galactic nucleus harbouring a massive black hole, and further studies are desirable via techniques such as numerical simulations.