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

Abstract

The dynamical evolution of binaries of intermediate-massive black holes (IMBHs, massive black holes with a mass ranging between $10^2$ and $10^4 M_{\odot}$) 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 LISA. We study this evolution in the presence of rotation in the cluster. The eccentricity is strongly connected to the initial IMBHs velocities, and values of $\sim 0.7$ up to 0.9 are reached for low initial velocities, while almost circular orbits result if the initial velocities are increased. A Monte Carlo study indicates that these sources will be detectable by a detector such as LISA with median signal to noise ratios of between 10 and 20 over a three year period, although some events had signal to noise ratios of 300 or greater. Furthermore, one should also be able to estimate the chirp-mass with median fractional errors of $10^{-4}$, reduced mass on the order of $10^{-3}$ and luminosity distance on the order of $10^{-1}$. Finally, these sources will have a median angular resolution in the LISA detector of about 3 square degrees, putting events firmly in the field of view of future electromagnetic detectors such as LSST.