[Paper Review] Systematics of black hole binary inspiral kicks and the slowness approximation

Richard H. Price, Gaurav Khanna+1 more|ScholarWorks @ UTRGV (The University of Texas Rio Grande Valley)|Apr 3, 2011

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper explains that the cancellation of black hole binary recoil kicks (antikicks) during merger is not due to gravitational wave specifics or multipole interactions, but arises generally from the slow variation of momentum flux compared to the radiation's oscillation period. The slowness approximation enables accurate late-time numerical simulations to predict net kicks with high fidelity, offering a robust, general framework for estimating recoil in binary black hole mergers.

ABSTRACT

During the inspiral and merger of black holes, the interaction of gravitational wave multipoles carries linear momentum away, thereby providing an astrophysically important recoil, or "kick" to the system and to the final black hole remnant. It has been found that linear momentum during the last stage (quasinormal ringing) of the collapse tends to provide an "antikick" that in some cases cancels almost all the kick from the earlier (quasicircular inspiral) emission. We show here that this cancellation is not due to peculiarities of gravitational waves, black holes, or interacting multipoles, but simply to the fact that the rotating flux of momentum changes its intensity slowly. We show furthermore that an understanding of the systematics of the emission allows good estimates of the net kick for numerical simulations started at fairly late times, and is useful for understanding qualitatively what kinds of systems provide large and small net kicks.

Motivation & Objective

• To understand the physical origin of the antikick phenomenon in black hole binary mergers, where post-plunge radiation cancels earlier inspiral kicks.
• To determine whether the cancellation is specific to gravitational waves, black holes, or multipole interactions, or a more general dynamical effect.
• To develop a systematic method for estimating net linear momentum radiated using late-time numerical simulations.
• To assess the validity and utility of the slowness approximation in modeling momentum emission during the inspiral phase.
• To explore the implications for numerical relativity and particle perturbation models in predicting final black hole recoil velocities.

Proposed method

• The authors apply the slowness approximation, treating the amplitude and frequency of momentum radiation as evolving slowly compared to the oscillation period of the radiation.
• They analyze equatorial binary orbits in particle perturbation models and numerical relativity, focusing on momentum emission in the orbital plane.
• The method involves integrating momentum flux from late times (e.g., t/M ≈ -100) and comparing results to full inspiral integrations, showing convergence.
• They use a rotating beam model of momentum radiation to explain how gradual changes in intensity and phase lead to antikick cancellation.
• The approach is extended to non-equatorial orbits using the Hilbert-Huang transform to extract non-constant, time-varying frequencies from late pre-plunge data.
• The analysis is validated by comparing results from particle perturbation models with numerical relativity simulations, particularly for high spin (a/M = 0.9) and small mass ratio (μ = 10⁻⁴) systems.

Experimental results

Research questions

• RQ1 Why does the quasinormal ringdown phase produce an antikick that cancels a significant portion of the inspiral kick?
• RQ2 Is the antikick cancellation a unique feature of gravitational waves, black holes, or multipole interference, or a more general dynamical phenomenon?
• RQ3 Can the slowness approximation be used to accurately estimate net momentum radiated when starting simulations late in the inspiral?
• RQ4 What conditions lead to strong cancellation (e.g., near-total) versus weak cancellation of the net kick?
• RQ5 How can the momentum radiation from non-equatorial, inclined orbits be modeled when multiple time-varying frequencies are present?

Key findings

• The antikick cancellation is not due to gravitational wave specifics or multipole interference, but arises generally from the slow variation of momentum flux relative to the radiation period.
• The slowness approximation provides a robust explanation for the cancellation, valid in both linearized and nonlinear regimes.
• Numerical simulations started as late as t/M ≈ -100 yield momentum estimates nearly identical to those from full inspiral integrations, demonstrating the method's efficiency.
• For a mass ratio μ = 10⁻² and spin a/M = 0.8, integration from t/M = -100 still produces a momentum estimate accurate within modeling precision.
• A 97% cancellation of the maximum kick was observed in particle perturbation models with a/M = 0.9 and μ = 10⁻⁴, consistent with numerical relativity results.
• Initial results suggest that the Hilbert-Huang transform can extract multiple non-constant frequencies from late pre-plunge radiation, enabling modeling of non-equatorial orbits.