Closing the gap to convergence of gravitoturbulence in local simulations

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 crit ∼ 10 Ω −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.

Fragmentation favoured in discs around higher mass stars

“…More recent work continues to indicate that fragmentation typically requires α ≈ 0.1 (Baehr et al 2017). We can't, however, rule out that there might be an element of stochasticity (Paardekooper 2012;Young & Clarke 2016;Klee et al 2017Klee et al , 2019, or an alternative mode of fragmentation (Young & Clarke 2015), that could sometimes lead to fragmentation for longer cooling times, or smaller effective α values, than this boundary value.…”

Direct Formation of Planetary Embryos in Self-gravitating Disks

“…It is important to consider that the resolution and initial conditions may have an effect on the results. Convergence is not a given, particularly in simulations that concern gravitational collapse (Meru & Bate 2011a;Paardekooper 2012), potentially due to effects of dimensionality (Baehr et al 2017) or other numerical factors (Deng et al 2017;Klee et al 2017Klee et al , 2019. Thus, we performed a simulation with double the grid resolution of the noBR_L_10 simulation and compared the mass distribution.…”