The statistics of the subhalo abundance of dark matter haloes
  We study the population statistics of the surviving subhaloes of LCDM dark
matter haloes using a set of very high resolution N-body simulations. These
include both simulations of representative regions of the Universe and
ultra-high resolution resimulations of individual dark matter haloes. We find
that more massive haloes tend to have a larger mass fraction in subhaloes. For
example, cluster size haloes typically have 7.5 percent of their mass within
R200 in substructures of fractional mass larger than 1e-5, which is 25 percent
higher than galactic haloes. There is, however, a large variance in the subhalo
mass fraction from halo to halo, whereas the subhalo abundance shows much
higher regularity. For dark matter haloes of fixed mass, the subhalo abundance
decreases by 30 percent between redshift 2 and 0. The subhalo abundance
function correlates with the host halo concentration parameter and formation
redshift. However, the intrinsic scatter is not significantly reduced for
narrow ranges of concentration parameter or formation redshift, showing that
they are not the dominant parameters that determine the subhalo abundance in a
halo.
