Parametric instability in warped astrophysical discs: growth, saturation and feedback
arXiv:2301.07176 · doi:10.1093/mnras/stad211
Abstract
Attempts to understand the dynamics of warped astrophysical discs have garnered significant attention, largely motivated by the growing catalogue of observed distorted systems. Previous studies have shown that the evolution of the warp is crucially regulated by the internal flow fields established by the undulating geometry. These are typically modelled as laminar horizontal, shearing flows which oscillate back and forth at approximately the orbital frequency. However this shearing motion is known to be susceptible to a hydrodynamic, parametric instability of inertial waves which might modify the warped dynamics. Whilst the linear growth phase is well understood, the subsequent nonlinear saturation combined with the self-consistent feedback onto the warp has not been studied. In this work, we implement a novel numerical setup using the recent ring model framework of Fairbairn and Ogilvie, within the Lagrangian code GIZMO. We formally identify several locally growing modes in the simulation, as predicted by a three-mode coupling analysis of the instability, and find decent agreement with the theoretical growth rates. We understand the saturation mechanism as a wave breaking process which suppresses the growth of shorter wavelength parametric couplings first, whilst allowing the longest mode to dominate the final quasi-steady, wavelike turbulence. The Reynolds stresses, transporting energy from the warp to the small scales, can be effectively modelled using a time-dependent, anisotropic viscous alpha model which closely captures the amplitude and phase evolution of the warp. Consequently, this model might help inform future global studies which are commonplace but typically don't resolve the parametric instability.
Accepted MNRAS, 22 pages, 17 figures
References in corpus (12)
- Smoothed Particle Hydrodynamics and Magnetohydrodynamics
- On the diversity and statistical properties of protostellar discs
- Chasing Shadows: Rotation of the Azimuthal Asymmetry in the TW Hya Disk
- Convergence of the critical cooling rate for protoplanetary disk fragmentation achieved; the key role of numerical dissipation of angular momentum
- Local and global dynamics of eccentric astrophysical discs
- Disc tearing: numerical investigation of warped disc instability
- Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets
- Hydrodynamic instability in eccentric astrophysical discs
- Parametric instability in a free evolving warped protoplanetary disc
- Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics
- Nonlinear dynamics of hydrodynamic tori as a model of oscillations and bending waves in astrophysical discs
- Hydrodynamics of warps in the local model of astrophysical discs