  Dark matter annihilation is proportional to the square of the density and is
especially efficient in places of highest concentration of dark matter, such as
dark matter spikes. The spikes are formed as a result of contraction of the
dark matter density profile caused by adiabatic growth of a supermassive black
hole at the center of the dark matter halo or subhalo. We revisit the relation
between the properties and mass functions of dark matter halos and spikes, and
propose alternative models for the density spikes that can potentially
contribute to the isotropic gamma-ray background.
