Accretion History of Subhalo Population now and then

In the standard model of structure formation galaxies reside in virialized dark matter haloes which extend much beyond the observational radius of the central system. The dark matter halo formation process is hierarchical, small systems collapse at high redshift and then merge together forming larger ones. In this work we study the mass assembly history of host haloes at different observation redshifts and the mass function of accreted satellites (haloes that merge directly on the main halo progenitor). We show that the satellite mass function is universal, both independent on the host halo mass and observation redshift. The satellite mass function also turn out to be universal once only satellites before or after the host halo formation redshift (time at which the main halo progenitor assembles half of its final mass) are considered. We show that the normalizations of these distributions are directly related to the main halo progenitor mass distributions before and after its formation, while their slope and the exponential high mass cut-off remain unchanged.