Destruction of small-scale dark matter clumps in the hierarchical structures and galaxies

A mass function of the small-scale dark matter clumps is calculated analytically in the standard cosmological scenario with an inflationary-produced primordial fluctuation spectrum and with a hierarchical clustering of small clumps into the larger ones. The main attention is given to the destruction of clumps by tidal interactions. The small-scale clumps are efficiently disrupted at early stages of structure formation starting from the time of clump detachment from the universe expansion. Only a small fraction of these clumps, 0.1-0.5 %, in each logarithmic mass interval $\Delta\ln M\sim1$ survives the stage of hierarchical clustering. The survived clumps can be further destructed in the galaxies by tidal interactions with stars. The detailed calculations for the tidal destruction of clumps by stars in the Galactic bulge, disk and halo are performed. The dominant contribution to the clump destruction is shown to be given by the tidal disruption in the collective gravitational field of the Galactic disc. The obtained results are important for calculations of dark matter annihilation signals in the Galaxy.