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 = m2/m1 = 10-4, where m1 and m2 are the masses of the primary and secondary hole, respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for q ? 10-3 the eccentricity growth rate becomes negative, i.e. the binary circularizes 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 circularization 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 massive black holes (IMBHs) inspiralling on to MBHs (e.g. a putative $10^3, m M-{odot }$ black hole inspiralling on to Sgr A∗).