  We investigate how the properties of massive black hole binaries influence
the observed properties of core galaxies. We compare the observed trend in
stellar mass deficit as a function of total stellar mass in the core galaxy
with predicted trends in IllustrisTNG. We calculate mass deficits in simulated
galaxies by applying sub-grid, post-processing physics based on the results of
literature N-body experiments. We find the median value of the posterior
distribution for the minimum binary mass ratio capable of creating a core is
0.7. For the gas mass fraction above which a core is erased we find a median
value of 0.6. Thus low mass ratio binaries do not contribute to core formation
and gas-rich mergers must lead to star formation within the nucleus, ultimately
erasing the core. Such constraints have important implications for the overall
massive black hole binary population, black hole-galaxy co-evolution, and the
origin of the gravitational wave background.
