Binaries of massive black holes in rotating clusters: dynamics, gravitational waves, detection and the role of eccentricity

The dynamical evolution of binaries of intermediate-mass black holes (IMBHs; massive black holes with a mass ranging between 102 and 104Msolar) in stellar clusters has recently received an increasing amount of attention. This is at least partially due to the fact that if the binary is hard enough to evolve to the phase at which it will start emitting gravitational waves (GWs) efficiently, there is a good probability that it will be detectable by future space-borne detectors like Laser Interferometer Space Antenna. We study this evolution in the presence of rotation in the cluster by carrying out a series of simulations of an equal-mass binary of IMBHs embedded in a stellar distribution with different rotational parameters. The survey indicates that eccentricities and inclinations are primarily determined by the initial conditions of the IMBHs and the influence of dynamical friction, even though they are finally perturbed by the scattering of field stars. In particular, the eccentricity is strongly connected to the initial IMBHs velocities, and values of ~0.7 up to 0.9 are reached for low initial velocities, while almost circular orbits result if the initial velocities are increased. Evidence suggests a dependency of the eccentricity on the rotation parameter. We found only weak changes in the inclination, with slight variations of the orientation of the angular momentum vector of the binary. Counter-rotation simulations yield remarkably different results in eccentricity. A Monte Carlo study indicates that these sources will be detectable by a detector such as Laser Interferometer Space Antenna (LISA) with median signal-to-noise ratios (SNR) of between 10 and 20 over a three-year period, although some events had SNR of 300 or greater. Furthermore, one should also be able to estimate the chirp mass with median fractional errors of 10-4, reduced mass of the order of 10-3 and luminosity distance of the order of 10-1. Finally, these sources will have a median angular resolution in the LISA detector of about 3 deg2, putting events firmly in the field of view of future electromagnetic detectors such as Large Synoptic Survey Telescope