Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics

TL;DR

This paper models nonlinear resonant warp dynamics in Keplerian discs using a novel nonlinear ring approach, revealing two regimes of warp evolution and identifying special precessing solutions with potential implications for energy dissipation.

Contribution

It introduces a new nonlinear ring model to analyze resonant warp dynamics in Keplerian discs, uncovering distinct regimes and special precessing solutions.

Findings

Identification of smooth modulation and bouncing regimes of warp evolution.

Development of an impulsive theory predicting retrograde and prograde precessing solutions.

Implications for energy dissipation and warp dynamics in astrophysical discs.

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 -- nonlinear 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 nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here we uncover two distinct nonlinear regimes as the warp amplitude is increased. Initially we find a smooth modulation theory which 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 generalised 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 which predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasise the essential activation of nonlinear 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.