Stellar hardening of massive black hole binaries: the impact of the host
  rotation
  Massive black hole binaries (MBHBs) with masses of ~ 10^4 to ~ 10^10 of solar
masses are one of the main targets for currently operating and forthcoming
space-borne gravitational wave observatories. In this paper, we explore the
effect of the stellar host rotation on the bound binary hardening efficiency,
driven by three-body stellar interactions. As seen in previous studies, we find
that the centre of mass (CoM) of a prograde MBHB embedded in a rotating
environment starts moving on a nearly circular orbit about the centre of the
system shortly after the MBHB binding. In our runs, the oscillation radius is
approximately 0.25 ( approximately 0.1) times the binary influence radius for
equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries
remain anchored about the centre of the host. The binary shrinking rate is
twice as fast when the binary CoM exhibits a net orbital motion, owing to a
more efficient loss cone repopulation even in our spherical stellar systems. We
develop a model that captures the CoM oscillations of prograde binaries; we
argue that the CoM angular momentum gain per time unit scales with the internal
binary angular momentum, so that most of the displacement is induced by stellar
interactions occurring around the time of MBHB binding, while the subsequent
angular momentum enhancement gets eventually quashed by the effect of dynamical
friction. The effect of the background rotation on the MBHB evolution may be
relevant for LISA sources, that are expected to form in significantly rotating
stellar systems.
