Non-linear resonant torus oscillations as a model of Keplerian disc warp dynamics

Abstract

ABSTRACT Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime – non-linear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel non-linear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here, we uncover two distinct non-linear regimes as the warp amplitude is increased. Initially, we find a smooth modulation theory that describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalized secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory that predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasize the essential activation of non-linear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.