Non-convergence of the critical cooling timescale for fragmentation of self-gravitating discs

TL;DR

This study investigates whether the critical cooling timescale for disc fragmentation converges with higher resolution in simulations, finding no convergence and questioning the existence of a universal critical value.

Contribution

The paper provides the first high-resolution SPH simulation study showing non-convergence of the critical cooling timescale for disc fragmentation.

Findings

Fragmentation occurs at longer cooling timescales with increased resolution.

No convergence of the critical cooling timescale beta_{crit} was observed.

Results challenge the use of cooling timescale as a universal criterion for fragmentation.

Abstract

We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results certainly suggest that beta_{crit} is larger than previously thought. However, the absence of convergence also questions whether or not a critical value exists. In light of these results, we caution against using cooling timescale or gravitational stress arguments to deduce whether gravitational instability may or may not have been the formation mechanism for observed planetary systems.