The impact of numerical oversteepening on the fragmentation boundary in self-gravitating disks

Abstract

Context. Whether or not a self-gravitating accretion disk fragments is still an open issue. There are many different physical and numerical explanations for fragmentation, but simulations often show a non-convergent behavior for ever better resolution. Aims. We aim to investigate the influence of different numerical limiters in Godunov type schemes on the fragmentation boundary in self-gravitating disks. Methods. We have compared the linear and non-linear outcomes in two-dimensional shearingsheet simulations using the VANLE ER and the SUPERBEE limiter. Results. We show that choosing inappropriate limiting functions to handle shock-capturing in Godunov type schemes can lead to an overestimation of the surface density in regions with shallow density gradients. The effect amplifies itself on timescales comparable to the dynamical timescale even at high resolutions. This is exactly the environment in which clumps are expected to form. The effect is present without, but scaled up by, self-gravity and also does not depend on cooling. Moreover it can be backtracked to a well known effect called oversteepening. If the effect is also observed in the linear case, the fragmentation limit is shifted to larger values of the critical cooling timescale.