The impact of numerical oversteepening on the fragmentation boundary in
  self-gravitating disks
  Context. It is still an open issue whether a self-gravitating accretion disk
fragments. There are many different physical and numerical explanations for
fragmentation, but simulations often show a non-convergent behavior for ever
better resolution.
  Aims. We investigate the influence of different numerical limiters in Godunov
type schemes on the fragmentation boundary in self- gravitating disks.
  Methods. We compare the linear and non-linear outcome in two-dimensional
shearingsheet simulations using the VANLEER 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, where 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.
