  By employing N-body simulations, we inestigate the formation of massive black
hole binaries (MBHBs) through the sinking of two massive black holes (MBHs)
during galaxy mergers. With different impact parameters and different central
stellar density of the progenitor galaxies, we analyze the orbits of the MBHs
from the beginning of the merger until the time when the bound MBHB forms.
Contrary to the previous theory that the timing of the dual MBHs entering their
dynamical radius is similar as the timing of the formation of the bound MBHB,
we find that these two timings could deviate when the central stellar density
of the progenitors galaxies are lower. On the other hand, when the central
stellar density of the progenitor galaxies is higher and the mergers have small
impact parameters, each MBHs would move directly into the core radius of the
other progenitor galaxies, and therefore cause a variation in the timings of
the MBHB formation.
