Mergers of Binary Primordial Black Holes in Evolving Dark Matter Halos

The influence of a dark matter halo around binary primordial black holes on the orbit evolution and the black hole merger rate is considered. Because of the nonspherical contraction of dark matter shells, each shell upon the first contraction passes through the halo center in the direction of the radius vector corresponding to zero angular momentum. Since the shell contraction is a continuous process, at each instant of time there is a nonzero dark matter density at the halo center. This density is determined by the influence of the tidal gravitational forces from inflationary density perturbations and from other primordial black holes. The scattering of dark matter particles by a pair of black holes leads to a loss of the energy of its orbital motion and to an accelerated pair merger. In the case of primordial black holes with masses \({\sim}\;30\;M_{\odot}\), the black hole merger rate in the presence of a dark matter halo is several times higher than that without such a halo.