During the coalescence of binary black holes , gravitational waves carry linear momentum away from the source , which results in the recoil of the center of mass .
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 \eta = \frac { m _ { 1 } m _ { 2 } } { ( m _ { 1 } + m _ { 2 } ) ^ { 2 } } \simeq 0.2 , i.e. , for a mass ratio m _ { 2 } / m _ { 1 } \simeq 0.38 .
Away from this optimal mass ratio , the recoil velocity decreases approximately proportionally to the scaling function \tilde { f } ( \eta ) = \eta ^ { 2 } \left ( 1 - 4 \eta \right ) ^ { 1 / 2 } \left ( 1.0912 - 1.04 % \eta + 2.92 \eta ^ { 2 } \right ) .
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 .