Simple procedures to reduce eccentricity of binary black hole simulations

Abstract

We present simple procedures to construct quasicircular initial data for numerical evolutions of binary black hole spacetimes. Our method consists of using the post-Newtonian (PN) theory in three ways: first to provide an initial guess for the initial momenta at 3.5PN order that implies low residual eccentricity, second to measure the resulting eccentricity, and third to calculate corrections to the momenta or initial separation that further reduce the eccentricity. Regarding the initial guess, we compare numerical evolutions in post-Newtonian theory to the postcircular and post-postcircular analytical approximations to quasicircular data. We discuss a robust fitting procedure to measure eccentricity from numerical simulations using the orbital frequency $\mathrm{\ensuremath{\Omega}}$, and derive from the quasi-Keplerian parametrization at 1PN order the correction factors for the tangential and radial momentum components required to reduce the measured eccentricity to zero. We first test our procedure integrating PN equations of motion at 3.5PN where low eccentric initial data are easily obtained, and then apply our method to sets of binary black hole numerical relativity simulations with different mass ratios ($q={m}_{2}/{m}_{1}=1,2,\dots{},8$), spin configurations, and separations. Our set of simulations contains nonspinning, spin-aligned, and precessing simulations. We observe that the iterative procedure produces low eccentric simulations with eccentricities of the order $\mathcal{O}({10}^{\ensuremath{-}4})$ with only one iteration. The simplicity of the procedure allows one to obtain low eccentric numerical relativity simulations easily and save computational resources. Moreover, the analytical PN formulas derived in this paper will be useful to generate eccentric hybrid waveforms.