The formation of galaxy stellar cores by the hierarchical merging of supermassive black holes

We investigate a hierarchical structure formation scenario in which galaxy stellar cores are created from the binding energy liberated by shrinking supermassive black hole (SMBH) binaries. The binary orbital decay heats the surrounding stars, eroding a preexisting 1/r^2 stellar cusp. We follow the merger history of dark matter halos and associated SMBHs via cosmological Monte Carlo realizations of the merger hierarchy from early times to the present in a LCDM cosmology. Massive black holes get incorporated through a series of mergers into larger and larger halos, sink to the center owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become supermassive, and form a binary system. Stellar dynamical processes drive the binary to harden and eventually coalesce. A simple scheme is applied in which the loss cone is constantly refilled and a constant density core forms due to the ejection of stellar mass. We find that a model in which the effect of the hierarchy of SMBH interactions is cumulative and cores are preserved during galaxy mergers produces at the present epoch a correlation between the `mass deficit' (the mass needed to bring a flat inner density profile to a 1/r^2 cusp) and the mass of the nuclear SMBH, with a normalization and slope comparable to the observed relation. Models in which the mass displaced by the SMBH binary is replenished after every major galaxy merger appear instead to underestimate the mass deficit observed in `core' galaxies.