Abstract
Binary supermassive black holes (SMBHs) are expected to form naturally during galaxy mergers. After the dynamical friction phase, when the two SMBHs become gravitationally bound to each other, and a brief stage of initial rapid hardening, the orbit gradually continues to shrink due to three-body interactions with stars that enter the loss cone of the binary. Using the stellar-dynamical Monte Carlo code RAGA, we explore the co-evolution of the binary SMBH and the nuclear star cluster in this slow stage, for various combinations of parameters (geometry of the star cluster, primary/secondary SMBH mass, initial eccentricity, inclusion of stellar captures/tidal disruptions). We compare the rates of stellar captures in galactic nuclei containing a binary SMBH to those of galaxies with a single SMBH. At early times, the rates are substantially higher in the case of a binary SMBH, but subsequently they drop to lower levels. Only in triaxial systems both the binary hardening rates and the capture rates remain sufficiently high during the entire evolution. We find that the hardening rate is not influenced by star captures, nor does it depend on eccentricity; however, it is higher when the difference between the black hole masses is greater. We confirm that the eccentricity of the binary tends to grow, which may significantly shorten the coalescence time due to earlier onset of gravitational-wave emission. We also explore the properties of the orbits entering the loss cone, and demonstrate that it remains partially full throughout the evolution in the triaxial case, but significantly depleted in the axisymmetric case. Finally, we study the distribution of ejected hypervelocity stars and the corresponding mass deficits in the central parts of the galaxies hosting a binary, and argue that the missing mass is difficult to quantify observationally.