An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral

We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial parameters by comparing the inspiral with post-Newtonian calculations. Our method is the first to be applied directly to the gravitational-wave (GW) signal, rather than the orbital motion. The GW signal is in general less contaminated by gauge effects, which, in moving-puncture simulations, limit orbital-motion-based measurements of the eccentricity to an uncertainty of $\Delta e \sim 0.002$, making it difficult to reduce the eccentricity below this value. Our new method can reach eccentricities below $10^{-3}$ in one or two iteration steps; we find that this is well below the requirements for GW astronomy in the advanced detector era. Our method can be readily adapted to any compact-binary simulation with GW emission, including black-hole-binary simulations that use alternative approaches, and neutron-star-binary simulations. We also comment on the differences in eccentricity estimates based on the strain $h$, and the Newman-Penrose scalar $\Psi_4$.