Numerical resolution limits on subhalo abundance matching
  Subhalo abundance matching (SHAM) inserts galaxies into dark matter only
simulations of the growth of cosmic structure in a way that requires minimal
assumptions about galaxy formation. A galaxy is placed at the potential minimum
of each distinct self-bound subhalo with a luminosity which is a monotonically
increasing function of the maximum mass (or circular velocity) attained over
the subhalo's earlier history. Galaxy and subhalo properties are linked by
matching model and observed luminosity functions. Simulated structures can then
be compared in detail with observation, for example, through galaxy correlation
statistics, group catalogues, or galaxy-galaxy lensing. Robust astrophysical
conclusions can be drawn from such a comparison only on scales which are
unaffected by the numerical limitations of the simulation. Here we compare
results for the Millennium Simulation (MS) with subhalos defined using the
SUBFIND to those obtained applying identical analysis to the much higher
resolution Millennium-II. Correlation statistics on scales between 200 kpc and
2 Mpc converge to within 20% only for subhalos with masses at infall
corresponding to at least 1000 simulation particles in the MS. Numerically
converged results can be obtained to much lower infall particle number, if
galaxies are followed even after their associated subhalos have been tidally
disrupted, as in most recent semi-analytic galaxy formation simulations. This
allows robust comparison between simulation and observation over a wider
dynamic range in mass than for a SHAM analysis which ignores such "orphan"
galaxies.
