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.
