Quasicircular Orbital Parameters for Numerical Relativity Revisited

TL;DR

This paper extends the calculation of quasicircular orbital parameters in post-Newtonian theory to 3.5PN order, reducing eccentricities in numerical relativity simulations and including limits for small mass ratios and spins.

Contribution

It provides higher-order PN formulas for orbital parameters, radial infall, and center of mass, improving initial data for binary black hole simulations.

Findings

Lower eccentricities achieved with 3.5PN initial data.

Systematic reduction of eccentricity by up to an order of magnitude.

Effective initial data for various spin and mass ratio configurations.

Abstract

In the post-Newtonian (PN) expansion, we extend the determination of quasicircular orbital parameters to be used by subsequent full numerical simulations to the 3.5PN order, and find that this leads to lower eccentricities, $e$, than with our previous method that used up to 3PN order. We also supplement the computation of the radial infall due to radiation reaction and the location of the center of mass to 3.5PN order, providing explicit formulas. In addition, we consider the small mass ratio limit by explicitly including the Schwarzschild and Kerr limits, the later in quasi-isotropic as well as in our standard use of ADMTT coordinates. We evolve binaries with a $q=1/16$ mass ratio by using 3PN, 3.5PN, 3.5PN+Schwarzschild, 3.5PN+KerrQISO and 3.5PN+KerrADMTT quasicircular data for three different configurations where the larger hole intrinsic spins are $\chi^z=-0.8$, $-0.4$ and $+0.8$. Using different measures of eccentricity from the black hole trajectories and from the waveform amplitudes and phases, we determine a systematic reduction of eccentricities with respect to the 3PN initial values by factors of up to an order of magnitude, and reaching the desired $e\sim10^{-3}$ threshold.