Oscillations of Static Discs around Schwarzschild Black Holes: Effect of Self-Gravitation

Abstract

Abstract The oscillations of accretion-disc matter about roughly circular motion may produce a quasi-periodic variation in the observed signal (Ipser 1996, AAA 65.067.047). They were studied theoretically on non-gravitating, test discs, in a pseudo-Newtonian manner as well as in general relativity, both in static and in stationary fields. The present paper shows how the radial profiles of oscillation frequencies can be modified by the self-gravity of the disc. Exact superpositions of a Schwarzschild black hole with the Lemos and Letelier (1994, AAA 61.067.077) annular discs (static thin discs obtained by inversion of the first Morgan-Morgan solution) are considered to be simple (static) models of an accretion system. Both the epicyclic and perpendicular frequencies are plotted against the Schwarzschild radius, the circumferential radius, and the proper distance from the horizon. The curves indicate that in the innermost parts more massive discs are more stable with respect to horizontal perturbations, whereas they are less stable with respect to vertical perturbations. In the case of a sequence of discs interpretable as counter-rotating particles on stable time-like circular geodesics and having their inner rims just on marginally stable circular orbits, oscillations of the inner parts get faster with increasing disc mass; the maximum of the epicyclic frequency, important for trapping of the low-frequency modes near the inner radius, moves to smaller radii and becomes somewhat higher.