A merger tree with microsolar mass resolution: application to ?-ray emission from subhalo population

The hierarchical growth of dark matter haloes, in which galaxies are hosted, has been studied and modelled using various approaches. In this paper, we use a modified version the Sheth & Lemson algorithm for a Λ cold dark matter power spectrum, and model the growth of a Milky Way sized halo with microsolar mass resolution, corresponding to the typical Jeans mass for a dark matter Weakly Interacting Massive Particle with mass of 100 GeV. We then compute the unevolved subhalo mass function and build up a Milky Way halo placing and evolving its satellites. This subhalo population is used to study the γ-ray emission from dark matter annihilation. In this case, the subhaloes which populate the host halo have been computed considering only progenitor haloes accreted by the main branch of the tree, so as to correctly treat the embedding of sub-subhaloes inside subhaloes. Each subhalo will indeed host at the present-time sub-subhaloes accreted when it was an isolated system. In order to compute the sub-subhalo population of a Milky Way dwarf galaxy, like Draco, and to study its γ-ray emission, we first estimate the Draco virial mass at merging redshift zm and then we run the merger tree from zm following the halo down to the dark matter Jeans mass. We then study the effect on the Fermi Large Area Telescope (GLAST) detectability for both subhaloes in the Milky Way and in Draco, and we show how subhaloes cannot be responsible for the boost factor needed for detection.