Assembly history of subhalo populations in galactic and cluster sized dark haloes

We make use of two suits of ultra high resolution N-body simulations of individual dark matter haloes from the Phoenix and the Aquarius Projects to investigate systematics of assembly history of subhaloes in dark matter haloes differing by a factor of $1000$ in the halo mass. We have found that real progenitors which built up present day subhalo population are relatively more abundant for high mass haloes, in contrast to previous studies claiming a universal form independent of the host halo mass. That is mainly because of repeated counting of the 're-accreted' (progenitors passed through and were later re-accreted to the host more than once) and inclusion of the 'ejected' progenitor population(progenitors were accreted to the host in the past but no longer members at present day) in previous studies. The typical accretion time for all progenitors vary strongly with the host halo mass, which is typical about $z \sim 5$ for the galactic Aquarius and about $z \sim 3$ for the cluster sized Phoenix haloes. Once these progenitors start to orbit their parent haloes, they rapidly lose their original mass but not their identifiers, more than $55$ ($50$) percent of them survive to present day for the Phoenix(Aquarius) haloes. At given redshift, survival fraction of the accreted subhalo is independent of the parent halo mass, whilst the mass-loss of the subhalo is more efficient in high mass haloes. These systematics results in similarity and difference in the subhalo population in dark matter haloes of different masses at present day.