Nonlinear behaviour of warped discs around a central object with a quadrupole moment

TL;DR

This study investigates the nonlinear dynamics of warped accretion discs around objects with quadrupole moments, using advanced hydrodynamical simulations to validate a theoretical model and explore disc stability and structure.

Contribution

It verifies a nonlinear bending-wave theory with high-resolution simulations and compares the performance of MFM and SPH methods in modeling warped discs.

Findings

MFM accurately maintains steady nonlinear warps in low-viscosity discs.

SPH suffers from severe numerical dissipation, degrading warp quality.

High-resolution simulations reveal parametric instability and ring formation.

Abstract

The nonlinear behaviour of low-viscosity warped discs is poorly understood. We verified a nonlinear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, Meshless Finite Mass (MFM), and also the Smoothed Particle Hydrodynamics (SPH) method, with up to 128M particles. For moderate nonlinearity, MFM maintains well the steady nonlinear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude nonlinear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a nonlinear steady state. However, no such state exists in our thin disc with an angular semi-thickness H/R = 0.02 when the outer tilt angle is beyond about 14 degrees. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme nonlinear deformation. Parametric instability is captured only in our highest-resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.