Nonlinear analysis of gravitational instability in a 3D gaseous disc

TL;DR

This paper proposes a nonlinear mechanism explaining how gravitationally stable astrophysical discs can develop turbulence through subcritical solitary equilibria, which may lead to instability and turbulence despite linear stability.

Contribution

It introduces analytically derived weakly nonlinear axisymmetric solitary equilibria in linearly stable 3D discs, revealing a nonlinear pathway to turbulence.

Findings

Existence of subcritical solitary equilibria near the instability threshold.

These equilibria are slightly more energetic than uniform discs.

Structures are likely unstable to non-axisymmetric perturbations.

Abstract

Astrophysical discs which are sufficiently massive and cool are linearly unstable to the formation of axisymmetric structures. In practice, linearly stable discs of surface density slightly below the threshold needed for this instability often form spiral structures, and can subsequently fragment or exhibit a state of self-sustained turbulence, depending on how rapidly the disc cools. This has raised the question of how such turbulence is possible in the linearly stable regime. We suggest a nonlinear mechanism for this phenomenon. We find analytically weakly nonlinear axisymmetric subcritical solitary equilibria which exist in linearly stable 3D discs that are close to the instability threshold. The energy of these 'soliton' solutions is only slightly higher than that of a uniform disc, and the structures themselves are expected to be unstable to non-axisymmetric perturbations. In this way, these subcritical solitary equilibria highlight a nonlinear instability and provide a possible pathway to a turbulent state in linearly stable discs.