  Massive black hole (MBH) binaries, formed as a result of galaxy mergers, are
expected to harden by dynamical friction and three-body stellar scatterings,
until emission of gravitational waves (GWs) leads to their final coalescence.
According to recent simulations, MBH binaries can efficiently harden via
stellar encounters only when the host geometry is triaxial, even if only
modestly, as angular momentum diffusion allows an efficient repopulation of the
binary loss cone. In this paper, we carry out a suite of N-body simulations of
equal-mass galaxy collisions, varying the initial orbits and density profiles
for the merging galaxies and running simulations both with and without central
MBHs. We find that the presence of an MBH binary in the remnant makes the
system nearly oblate, aligned with the galaxy merger plane, within a radius
enclosing 100 MBH masses. We never find binary hosts to be prolate on any
scale. The decaying MBHs slightly enhance the tangential anisotropy in the
centre of the remnant due to angular momentum injection and the slingshot
ejection of stars on nearly radial orbits. This latter effect results in about
1% of the remnant stars being expelled from the galactic nucleus. Finally, we
do not find any strong connection between the remnant morphology and the binary
hardening rate, which depends only on the inner density slope of the remnant
galaxy. Our results suggest that MBH binaries are able to coalesce within a few
Gyr, even if the binary is found to partially erase the merger-induced
triaxiality from the remnant.
