Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques

TL;DR

This paper combines numerical relativity and perturbative methods to accurately model gravitational waves from intermediate-mass-ratio black hole binaries, validating the approach with high waveform overlaps.

Contribution

It introduces a hybrid approach that integrates full numerical simulations with perturbative techniques, including spin effects, for intermediate-mass-ratio black hole mergers.

Findings

High waveform overlaps (>98%) between numerical and perturbative models.

Effective extension of perturbative formalism to include black hole spins.

Validated methods for different mass ratios and initial conditions.

Abstract

We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios q=1/10 and q=1/15 from different initial separations and for different finite-difference resolutions. In order to perform those full numerical runs, we adapt the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode frequencies, where we find good agreement for spins |a/M|<0.3. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading (l,m)=(2,2) and (3,3) modes, and 98.3% for the nonleading (2,1) mode in the q=1/10 case, which includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian, full numerical, and geodesic trajectories.