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 increasing simulation resolution, finding no convergence and suggesting the critical value may be longer than previously estimated.

Contribution

The paper provides the highest resolution simulations to date, revealing non-convergence in the critical cooling timescale for self-gravitating disc fragmentation.

Findings

Fragmentation occurs at longer cooling timescales with higher resolution.

No convergence observed in the critical cooling timescale.

Questions the existence of a universal critical cooling timescale.

Abstract

We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics 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 suggest that at the very least, the critical value of the cooling timescale is longer than previously thought. However, the absence of convergence also raises the question of 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.