Study of the Intermediate Mass Ratio Black Hole Binary Merger up to 1000:1 with Numerical Relativity

TL;DR

This paper demonstrates that current numerical relativity methods can accurately simulate black hole mergers with mass ratios up to 1000:1, aiding future gravitational wave detection and analysis.

Contribution

It provides the first proof that numerical relativity can handle extremely high mass ratio black hole mergers, matching perturbative results.

Findings

High agreement between numerical and perturbative results for gravitational waves.

Established minimal resolutions needed for accurate low-amplitude wave simulations.

Demonstrated numerical convergence for extreme mass ratio simulations.

Abstract

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation (3G) gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, $m_1^p/m_2^p = 1/7, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024$, with the small hole starting from rest at a proper distance $D\approx13M$. We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.