Anatomy of the binary black hole recoil: A multipolar analysis

Abstract

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.

28 pages, 20 figures, submitted to PRD; v2: minor revisions from referee report

References in corpus (6)

• Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
• Supermassive recoil velocities for binary black-hole mergers with antialigned spins
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Observable Signatures of a Black Hole Ejected by Gravitational Radiation Recoil in a Galaxy Merger
• Modeling kicks from the merger of non-precessing black-hole binaries
• Binary black hole mergers: large kicks for generic spin orientations

Cited by in corpus (7)

• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
• Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
• The spin expansion for binary black hole merger: new predictions and future directions
• Multipolar analysis of spinning binaries
• Numerical Relativity meets Data Analysis: Spinning Binary Black Hole Case
• Estimating total momentum at finite distances