Parameter control for eccentric, precessing binary black hole simulations with SpEC

TL;DR

This paper presents a new iterative parameter control method for numerical relativity simulations of binary black holes, enabling precise setting of orbital eccentricity and spin directions with high accuracy.

Contribution

It extends existing techniques to control both orbital and spin parameters in binary black hole simulations using SpEC, achieving rapid convergence.

Findings

Achieves -3 eccentricity convergence within 7 iterations

Controls spin directions within b0 accuracy

Applicable to binaries with mass ratios up to 3, eccentricities up to 0.65

Abstract

Numerical relativity simulations of merging black holes provide the most accurate description of the binary dynamics and the emitted gravitational wave signal. However, practical considerations such as imperfect initial data and initial parameters mean that achieving target parameters, such as the orbital eccentricity or the black hole spin directions, at the beginning of the usable part of the simulation is challenging. In this paper, we devise a method to produce simulations with specific target parameters, namely the Keplerian orbital parameters-eccentricity, semimajor axis, mean anomaly-and the black hole spin vectors using SpEC. The method is an extension of the current process for achieving vanishing eccentricity and it is based on a parameter control loop that iteratively numerically evolves the system, fits the orbit with analytical post-Newtonian equations, and calculates updated input parameters. Through SpEC numerical simulations, we demonstrate $\lesssim 10^{-3}$ and $O(\rm degree)$ convergence for the orbital eccentricity and the spin directions respectively in $\leq7$ iterations. These tests extend to binaries with mass ratios $q \leq 3$, eccentricities $e \leq 0.65$, and spin magnitudes $|\chi | \leq 0.75$. Our method for controlling the orbital and spin parameters of numerical simulations can be used to produce targeted simulations in sparsely covered regions of the parameter space or study the dynamics of relativistic binaries.