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We study the dynamical evolution of eccentric massive black hole binaries(MBHBs) interacting with unbound stars by means of an extensive set of threebody scattering experiments. Compared to previous studies, we extend theinvestigation 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. Contraryto a simple extrapolation from higher mass ratios, we find that for $q\lesssim10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\itcircularises} as it shrinks. This behaviour is due to the subset of interactingstars captured in metastable counter-rotating orbits; those stars tend toextract angular momentum from the binary, promoting eccentricity growth for$q>10^{-3}$, but tend to inject angular momentum into the binary driving ittowards circularisation for $q<10^{-3}$. The physical origin of this behaviourrequires a detailed study of the orbits of this subset of stars and iscurrently under investigation. Our findings might have important consequencesfor intermediate MBHs (IMBHs) inspiralling onto MBHs (e.g. a putative $10^3\rmM_{\odot}$ black hole inspiralling onto SgrA$^*$).

On the eccentricity evolution of massive black hole binaries in stellar backgrounds