Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: testing radiation reaction and waveform

We provide a systematic analysis of the multipolar gravitational waveform, energy and angular momentum fluxes emitted by a nonspinning test particle orbiting a Kerr black hole along equatorial, eccentric orbits. These quantities are computed by numerically solving the Teukolsky equation in the time domain and are then used to test and improve the radiation reaction (and waveform) of an effective-one-body (EOB) model. Eccentricity is incorporated into EOB by replacing the quasi-circular Newtonian (or leading-order) prefactors in the EOB-factorized multipolar waveform (and fluxes) with their generic counterparts. The comparison between numerical and analytical quantities is carried out over a large portion of the parameter space, notably for orbits close to the separatrix and with high eccentricities. The analytical model agrees to $\sim 1\%$ with the numerical data for orbits with moderate eccentricities ($e\lesssim 0.3$) and moderate spins ($\hat{a}\lesssim 0.5$), although this increases up to $\sim 33\%$ for large, positive, black hole spins ($\sim 0.9$) and large eccentricities ($\sim 0.9$). For moderate eccentricities, the new EOB fluxes can be used to drive the dynamics through the nonadiabatic transition from eccentric inspiral to plunge, merger and ringdown, thus providing accurate an description of the merger. We also show that the same technique can be applied to hyperbolic encounters. In general, our approach to radiation reaction for eccentric inspirals should be seen as a first step toward EOB modelization of extreme-mass-ratio-inspirals waveforms for LISA.