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.