Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis

Abstract

Building up on previous work, we present a new calculation of the gravitational wave (GW) emission generated during the transition from quasi-circular inspiral to plunge, merger and ringdown by a binary system of nonspinning black holes, of masses $m_1$ and $m_2$, in the extreme mass ratio limit, $m_1{m}_2\ll (m_1+m_2{)}^2$. The relative dynamics of the system is computed {\it without making any adiabatic approximation} by using an effective one body (EOB) description, namely by representing the binary by an effective particle of mass $\mu =m_1{m}_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M=m_1+m_2$ and submitted to an $Ø(\nu )$ 5PN-resummed analytical radiation reaction force, with $\nu =\mu /M$. The gravitational wave emission is calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach (valid in the limit $\nu \ll 1$). We consider three mass ratios, $\nu =10^{-2},10^{-3},10^{-4}$,and we compute the multipolar waveform up to $\ell =8$. We estimate energy and angular momentum losses during the quasi-universal and quasi-geodesic part of the plunge phase and we analyze the structure of the ringdown. We calculate the gravitational recoil, or "kick", imparted to the merger remnant by the gravitational wave emission and we emphasize the importance of higher multipoles to get a final value of the recoil $v/(c{\nu }^2)=0.0446$. We finally show that there is an {\it excellent fractional agreement} ($\sim 10^{-3}$) (even during the plunge) between the 5PN EOB analytically-resummed radiation reaction flux and the numerically computed gravitational wave angular momentum flux. This is a further confirmation of the aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals, as needed for the future space-based LISA gravitational wave detector.

20 pages, 12 figures. Version published in Phys. Rev. D

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