# Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity

## TL;DR

This paper develops a method using post-Newtonian approximations to set initial conditions for black hole binary simulations that result in low-eccentricity inspirals, improving the accuracy of numerical relativity models.

## Contribution

It introduces a new approach combining 3PN Hamiltonian and high-order radiation reaction expressions to generate initial data with minimal eccentricity for black hole binaries.

## Key findings

- Using 3PN Hamiltonian and high-order radiation reaction yields the lowest eccentricity.
- The method surpasses previous inspiral data accuracy based on 3PN and 4PN evolutions.
- Applicable to spinning, nonprecessing, unequal mass binaries.

## Abstract

We use post-Newtonian (PN) approximations to determine the initial orbital and spin parameters of black hole binaries that lead to low-eccentricity inspirals when evolved with numerical relativity techniques. In particular, we seek initial configurations that lead to very small eccentricities at small separations, as is expected for astrophysical systems. We consider three cases: (i) quasicircular orbits with no radial velocity, (ii) quasicircular orbits with an initial radial velocity determined by radiation reaction, and (iii) parameters obtained form evolution of the PN equations of motion from much larger separations. We study seven cases of spinning, nonprecessing, unequal mass binaries. We then use several definitions of the eccentricity, based on orbital separations and waveform phase and amplitude, and find that using the complete 3PN Hamiltonian for quasicircular orbits to obtain the tangential orbital momentum, and using the highest-known-order radiation reaction expressions to obtain the radial momentum, leads to the lowest eccentricity. The accuracy of this method even exceeds that of inspiral data based on 3PN and 4PN evolutions.