Non-convergence of the critical cooling timescale for fragmentation of
  self-gravitating discs
  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.
