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We construct evolutionary tracks for massive black hole binaries (MBHBs)embedded in a surrounding distribution of stars. The dynamics of the binary isevolved by taking into account the erosion of the central stellar cusp bound tothe massive black holes, the scattering of unbound stars feeding the binaryloss cone, and the emission of gravitational waves (GWs). Stellar dynamics istreated in a hybrid fashion by coupling the results of numerical 3-bodyscattering experiments of bound and unbound stars to an analytical frameworkfor the evolution of the stellar density distribution and for the efficiency ofthe binary loss cone refilling. Our main focus is on the behaviour of thebinary eccentricity, in the attempt of addressing its importance in the mergerprocess and its possible impact for GW detection with the planned LaserInterferometer Space Antenna ({\it LISA}), and ongoing and forthcoming pulsartiming array (PTA) campaigns. We produce a family of evolutionary tracksextensively sampling the relevant parameters of the system which are the binarymass, mass ratio and initial eccentricity, the slope of the stellar densitydistribution, its normalization and the efficiency of loss cone refilling. Wefind that, in general, stellar dynamics causes a dramatic increase of the MBHBeccentricity, especially for initially already mildly eccentric and/or unequalmass binaries. When applied to standard MBHB population models, our resultspredict eccentricities in the ranges $10^{-3}-0.2$ and $0.03-0.3$ for sourcesdetectable by {\it LISA} and PTA respectively. Such figures may have asignificant impact on the signal modelling, on source detection, and on thedevelopment of parameter estimation algorithms.

the astrophysical journal

Self consistent model for the evolution of eccentric massive black hole  binaries in stellar environments: implications for gravitational wave  observations