Intermediate-mass-ratio black hole binaries II: Modeling Trajectories and Gravitational Waveforms

TL;DR

This paper develops accurate models for trajectories and gravitational waveforms of intermediate-mass-ratio black hole binaries, enabling efficient waveform generation for gravitational wave detection.

Contribution

It introduces new fitting functions for black hole trajectories and demonstrates high-accuracy waveform modeling using perturbation theory, reducing reliance on extensive numerical simulations.

Findings

Achieved ~99.5% match between numerical and perturbative waveforms.

Validated the feasibility of efficient waveform bank generation in the intermediate-mass-ratio regime.

Provided fitting functions combining post-Newtonian and geodesic aspects for trajectory modeling.

Abstract

We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.5% for the leading (l,m)=(2,2) mode between the numerical relativity and perturbative waveforms. Nonleading modes have similarly high matches. We thus prove the feasibility of efficiently generating a bank of gravitational waveforms in the intermediate-mass-ratio regime using only a sparse set of full numerical simulations.