Building initial conditions for generic binary black-hole evolutions which are not affected by initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists of evolving the binary black hole for a couple of orbits, estimating the resulting eccentricity, and then restarting the simulation with corrected initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. For single-spin binary black holes these oscillations are a direct consequence of monopole-quadrupole interactions. However, spin-induced oscillations occur at approximately twice the orbital frequency, and therefore can be distinguished and disentangled from the initial spurious eccentricity which occurs at approximately the orbital frequency. Taking this into account, we develop a new eccentricity-removal procedure based on the derivative of the orbital frequency and find that it is rather successful in reducing the eccentricity measured in the orbital frequency to values less than ${10}^{-4}$ when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5, and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant $l=2$, $m=2$ mode.

• Received 17 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.104034