Closing the gap to convergence of gravitoturbulence in local simulations

TL;DR

This study identifies a nearly converged cooling timescale for fragmentation in self-gravitating disks using high-resolution simulations, providing a clear criterion for convergence relevant to planet and star formation.

Contribution

It establishes a converged critical cooling timescale for fragmentation and links this to the spectral behavior of physical quantities at critical length scales.

Findings

Critical cooling timescale for fragmentation: ~10 Ω^{-1}

Spectral analysis confirms convergence at specific length scales

Numerical deviations occur below the critical length scales

Abstract

Aims. Our goal is to find a converged cooling limit for fragmentation in self-gravitating disks. This is especially interesting for the formation of planets, brown dwarfs or stars and the growth of black holes. While investigating the limit, we want to give a clear criterion for the state of convergence. Methods. We run two-dimensional shearingsheet simulations with the hydrodynamic package Fosite at high resolutions. Thereby resolution and limiters are altered. Subsequently, we investigate the spectra of important physical quantities at the length scales where fragmentation occurs. In order to avoid prompt fragmentation at high resolutions we start these simulations with a fully developed gravitoturbulent state obtained at a lower resolution. Results. We show nearly converged results for fragmentation with a critical cooling timescale $t_{\mathrm{crit}} \sim 10\,\Omega^{-1}$ . We can backtrace this claim by investigating the spectra of relevant physical variables at length scales around and below the pressure scale height. We argue that well behaved results cannot be expected if counteracting quantities are varying too much on these critical length scales, either by change of resolution or numerical method. A comparison of fragmentation behaviour with the related spectra reveals that simulations behave similar, if the spectra are converged to the length scales where self-gravity leads to instabilities. Observable deviations in the results obtained with different numerical setup are confined to scales below these critical length scales.