Hierarchical Merger of Primordial Black Holes in Dwarf Galaxies

We study the merger history of primordial black holes (PBHs) in a scenario where they represent the dominant dark matter component of a typical dwarf galaxies' core. We investigate the possibility of a sequence of collisions resulting in a hierarchical merger of black holes and look at the final mass spectrum in such {\it clusters}, which initially present a monochromatic (single-mass) PBH population. Our study shows that the merging process results in the transfer of about $40\%$ of the total mass of the core to the merger products regardless of the initial mass of PBHs, with about $5\%$ of energy radiated out in the form of gravitational waves. We find that, in the lighter mass limit, black holes up to eight times more massive than the original population can be formed within a Hubble time.