Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach

TL;DR

This paper uses the Effective One Body approach to estimate gravitational recoil during the late inspiral and plunge of non-spinning binary black holes. It identifies a brief, non-adiabatic burst of linear momentum flux near the plunge as the key driver of the terminal kick and develops a framework to compute this recoil by integrating a quasi-Newtonian flux within EOB coordinates, with 2PN corrections and a transition to ring-down via quasi-normal modes. The authors find a best-guess terminal recoil of about 74 km/s (with a flux correction factor tilde{F} ≈ 1.35), but demonstrate a substantial uncertainty range (roughly 49–172 km/s) depending on the momentum-flux modeling and plunge-to-ring-down matching, signaling the need for further refinement. The study underscores the sensitivity of recoil predictions to plunge dynamics and provides a path for extending the analysis to spinning and eccentric binaries, with potential astrophysical implications for black hole retention in galaxies and high-redshift black hole formation.

Abstract

Using the Effective One Body approach, that includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of non-spinning black holes of comparable masses moving in quasi-circular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a ``burst'' of linear momentum flux emitted slightly before coalescence. When using the most natural expression for the linear momentum flux during the plunge, together with a Taylor-expanded $(v/c)^4$ correction factor, we find that the maximum value of the terminal recoil is $\sim 74$ km/s and occurs for a mass ratio $m_2/m_1 \simeq 0.38$. We comment, however, on the fact that the above `best bet estimate' is subject to strong uncertainties because the location and amplitude of the crucial peak of linear momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the Effective One Body approach are no longer justified. Changing the analytical way of estimating the linear momentum flux, we find maximum recoils that range between 49 and 172 km/s. (Abridged)