Exploring the small mass ratio binary black hole merger via Zeno's dichotomy approach

TL;DR

This paper conducts high-precision simulations of binary black hole mergers with very small mass ratios, extending previous work to 1/128, and refines phenomenological models for gravitational wave predictions.

Contribution

It introduces a Zeno's dichotomy inspired approach to simulate extremely small mass ratio black hole mergers and improves the accuracy of waveform models.

Findings

Successful simulation of 1/128 mass ratio mergers with detailed convergence analysis.

Validation of phenomenological formulas within 2% accuracy in the particle limit.

Enhanced fitting coefficients for gravitational waveform models.

Abstract

We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=m_1/m_2=1/15$ nonspinning case, we apply additional mesh refinements levels around the smaller hole horizon to reach successively the $q=1/32$, $q=1/64$, and $q=1/128$ cases. Roughly a linear computational resources scaling with $1/q$ is observed on 8-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: its peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients.