Eccentricity evolution of massive black hole binaries from formation to coalescence

Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models highly uncertain. A major difficulty stems from necessity model BHB scale merger that inspiral. Of particular relevance GW timescale is binary eccentricity. Here we present a self-consistent numerical study eccentricity BHBs formed massive gas-free mergers early stages hardening phase, followed by semi-analytical down coalescence. We find unbound pair largely determined initial orbit. It systematically decreases during dynamical friction phase. The at formation affected stochasticity noise owing encounters with stars, but preserves strong correlation orbital Binding holes phase characterised perturbations, quantitative definition time formation. During increases minor mergers, unless approximately circular, remains unchanged agreement predictions isotropic scattering experiments. Coalescence times due emission gas-poor non-rotating ellipticals <~0.5 Gyr large eccentricities (0.5 < e 0.9) typical galaxy simulations.