Galaxy Core Formation by Supermassive Black Hole Binaries: The Importance of Realistic Initial Conditions and Galaxy Morphology

The binding energy liberated by the coalescence of supermassive black hole (SMBH) binaries during galaxy mergers is thought to be responsible for the low density cores often found in bright elliptical galaxies. We use high-resolution $N$-body and Monte Carlo techniques to perform single and multi-stage galaxy merger simulations and systematically study the dependence of the central galaxy properties on the binary mass ratio, the slope of the initial density cusps, and the number of mergers experienced. We study both the amount of depleted stellar mass (or ``mass deficit'), $M_{\rm def}$, and the radial extent of the depleted region, $r_{\rm b}$. We find that $r_{\rm b}\simeq r_{\rm SOI}$ and that $M_{\rm def}$ varies in the range $0.5$ to $4M_{\bullet}$, with $r_{\rm SOI}$ the influence radius of the remnant SMBH and $M_{\bullet}$ its mass. The coefficients in these relations depend weakly on the binary mass ratio and remain remarkably constant through subsequent mergers. We conclude that the core size and mass deficit do not scale linearly with the number of mergers, making it hard to infer merger histories from observations. On the other hand, we show that both $M_{\rm def}$ and $r_{\rm b}$ are sensitive to the morphology of the galaxy merger remnant, and that adopting spherical initial conditions, as done in early work, leads to misleading results. Our models reproduce the range of values for $M_{\rm def}$ found in most observational work, but span nearly an order of magnitude range around the true ejected stellar mass.