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 solving numerically the Teukolsky equation in the time domain using Teukode and are then used to establish the reliability of a recently introduced prescription to deal with eccentricity-driven effects in the radiation reaction (and waveform) of the effective-one-body (EOB) model. The prescription relies on the idea of incorporating these effects by replacing the quasicircular Newtonian (or leading-order) prefactors in the EOB-factorized multipolar waveform (and fluxes) with their generic counterparts. To reliably account for strong-field regimes, standard factorization and resummation procedures had to be implemented also for the circular sector of l = 7 and l = 8 waveform multipoles. 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 fluxes agree to similar to 2% with the numerical data for orbits with moderate eccentricities (e less than or similar to 0.3) and moderate spins ((a) over cap less than or similar to 0.5), although this increases up to similar to 33% for large, positive, black hole spins (similar to 0.9) and large eccentricities (similar to 0.9). Similar agreement is also found for the waveform. For moderate eccentricities, the EOB fluxes can be used to drive the test-particle dynamics through the nonadiabatic transition from eccentric inspiral to plunge, merger, and ringdown. Over this dynamics, we construct a complete EOB waveform, including merger and ringdown, that shows an excellent phasing and amplitude agreement with the numerical one. 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.