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 the gravitational recoil velocity during binary black hole coalescence, highlighting the importance of a momentum flux burst before merger and providing a range of recoil velocities with uncertainties.

Contribution

It introduces a method to compute recoil velocities during black hole mergers using the EOB approach, including a new estimate for the maximum recoil and analysis of uncertainties.

Findings

Maximum recoil velocity ~74 km/s for certain mass ratios.

Recoil velocities range between 49 and 172 km/s depending on assumptions.

A key momentum flux burst occurs just before coalescence.

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)