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

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.

31 pages, 33 figures revtex 4, Published version. Several fixes throughout

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• Orbital Evolution of Extreme-Mass-Ratio Black-Hole Binaries with Numerical Relativity
• Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• Modeling maximum astrophysical gravitational recoil velocities
• Maximum black-hole spin from quasi-circular binary mergers
• Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild
• Modeling Gravitational Recoil Using Numerical Relativity
• Resonant recoil in extreme mass ratio binary black hole mergers
• Perturbative effects of spinning black holes with applications to recoil velocities