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

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.

Parametric instability in warped astrophysical discs: growth, saturation, and feedback

“…However, observationally significant distortions will inevitably incur the nonlinear dynamics of warped discs. Our previous analytical efforts tried to gain a handle on such large amplitude warped dynamics and predicted the activation of strongly compressive vertical, bouncing motions twice per orbit for a tilting ring (Fairbairn & Ogilvie 2021b). It is unclear how this background flow would support the growth of the parametric instability or whether the turbulence would quickly disrupt the bouncing.…”

“…Furthermore, efforts to understand the resonant Keplerian, inviscid regime have been explored by Ogilvie (2006) who developed evolutionary equations which follow a propagating, weakly nonlinear bending wave. More recently, Fairbairn & Ogilvie (2021a) have proposed a novel local ring model which also predicts the fully nonlinear extension of precessing bending modes (Fairbairn & Ogilvie 2021b). Despite all these efforts, the theories typically simplify matters by assuming laminar internal flows.…”

“…In this work we motivate our numerical setup, based on the ring model developed in Fairbairn & Ogilvie (2021a) and Fairbairn & Ogilvie (2021b), hereafter FOA and FOB respectively. This framework proved useful when investigating nonlinear solutions for warped disc dynamics and allows one to consider the self-consistent evolution of warp in the troublesome Keplerian regime where resonances complicate the dynamics.…”

Circumbinary Accretion: From Binary Stars to Massive Binary Black Holes

“…Protoplanetary disks around young binary stars (with α ∼ 10 −4 -10 −2 , h ≳ 0.05, and r/a b ≳ a few) generally satisfy these conditions (Foucart & Lai 2013). The nonlinear behavior of low-viscosity warped disks is complicated and poorly understood owing to the resonant excitation of vertical "breathing" motions (Fairbairn & Ogilvie 2021) and a parametric instability associated with the inertial waves (Gammie et al 2000, Ogilvie & Latter 2013, Paardekooper & Ogilvie 2019, Deng et al 2021, Deng & Ogilvie 2022.…”

Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks

“…These oscillations were also seen in the thick, tilted disk simulations of Fragile & Blaes (2008), and were recently computed analytically. Fairbairn & Ogilvie (2021b) developed a theory of oscillating fluid tori that can describe annuli of warped disks, and then in Fairbairn & Ogilvie (2021a) they applied this theory to nonlinear warps in inviscid, Keplerian disks. They identified a bouncing regime above a critical warp amplitude, leading to large-scale height variations (Figure 2 of Fairbairn & Ogilvie 2021a) that are remarkably similar to those seen here.…”