Abstract

Astrophysical discs encircling a central mass are ubiquitous in a variety of contexts – galactic, stellar and planetary. In many instances, such discs are observed to contain a total mass much less than that of the dominant central object. Despite this fact, discs – through their gravity – can play an important dynamical role in the orbital evolution of their constituent particles, as well as external objects (e.g. test-particles), by driving orbital precession and exchange of angular momentum over long (secular) time-scales. Thus, analytic quantification of the secular gravitational effects due to discs represents a vital necessity. One of the direct means for achieving this goal relies on the well-known Laplace-Lagrange theory. Nevertheless, this approach is ill-posed as it results in the divergence of the disc potential. This divergence has motivated the development of alternative approaches: one that resorts to softened forms of gravity (i.e. modifying the Newtonian potential with the introduction of an ad hoc softening parameter), and another which – by construction – does not suffer from the classical singularity inherent to Laplace-Lagrange theory.

In this talk, I will introduce these two methods and present results indicating that softened disc potentials can reproduce the expected secular dynamics of test-particles provided that the softening prescription (1) is implemented properly, and (2) satisfies certain mathematical and physical conditions. Building up on this finding, I will present preliminary results touching on the outstanding question pertinent to the sustenance of rigidly precessing self-gravitating eccentric discs such as the inferred stellar disc in the centre of M31 galaxy.