# Nonlinear outcome of gravitational instability in an irradiated protoplanetary disc

## TL;DR

This study uses 3D radiation hydrodynamics simulations to explore how gravitational instability in irradiated protoplanetary discs leads to either fragmentation or gravito-turbulence, depending on surface density and radius.

## Contribution

It provides a detailed analysis of the nonlinear outcomes of gravitational instability, identifying key boundaries and conditions for fragmentation versus turbulence in protoplanetary discs.

## Key findings

- Fragmentation occurs at radii around 75 AU when cooling is rapid.
- Higher surface density leads to more unstable, fragmenting discs.
- Short cooling times can trigger fragmentation even with gravito-turbulence.

## Abstract

Using local three dimensional radiation hydrodynamics simulations, the nonlinear outcome of gravitational instability in an irradiated protoplanetary disc is investigated in a parameter space of the surface density $\Sigma$ and the radius $r$. Starting from laminar flow, axisymmetric self-gravitating density waves grow first. Their self-gravitating degree becomes larger when $\Sigma$ is larger or the cooling time is shorter at larger radii. The density waves eventually collapse owing to non-axisymmetric instability, which results in either fragmentation or gravito-turbulence after a transient phase. The boundaries between the two are found at $r \sim 75$ AU as well as at the $\Sigma$ that corresponds to the initial Toomre's parameter of $\sim 0.2$. The former boundary corresponds to the radius where the cooling time becomes short, approximating unity. Even when gravito-turbulence is established around the boundary radius, such a short cooling time inevitably makes the fluctuation of $\Sigma$ large enough to trigger fragmentation. On the other hand, when $\Sigma$ is beyond the latter boundary (i.e. the initial Toomre's parameter is less than $\sim 0.2$), the initial laminar flow is so unstable against self-gravity that it evolves into fragmentation regardless of the radius or, equivalently, the cooling time. Runaway collapse follows fragmentation when the mass concentration at the centre of a bound object is high enough that the temperature exceeds the H$_2$ dissociation temperature.