On the eccentricity evolution of massive black hole binaries in stellar
  backgrounds
  We study the dynamical evolution of eccentric massive black hole binaries
(MBHBs) interacting with unbound stars by means of an extensive set of three
body scattering experiments. Compared to previous studies, we extend the
investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and
$m_2$ are the masses of the primary and secondary hole respectively. Contrary
to a simple extrapolation from higher mass ratios, we find that for $q\lesssim
10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it
circularises} as it shrinks. This behaviour is due to the subset of interacting
stars captured in metastable counter-rotating orbits; those stars tend to
extract angular momentum from the binary, promoting eccentricity growth for
$q>10^{-3}$, but tend to inject angular momentum into the binary driving it
towards circularisation for $q<10^{-3}$. The physical origin of this behaviour
requires a detailed study of the orbits of this subset of stars and is
currently under investigation. Our findings might have important consequences
for intermediate MBHs (IMBHs) inspiralling onto MBHs (e.g. a putative $10^3\rm
M_{\odot}$ black hole inspiralling onto SgrA$^*$).
