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We propose an improved analytical model for the horizon-absorbedgravitational-wave energy flux of a small body in circular orbit in theequatorial plane of a Kerr black hole. Post-Newtonian (PN) theory provides ananalytical description of the multipolar components of the absorption fluxthrough Taylor expansions in the orbital frequency. Building on previous work,we construct a mode-by-mode factorization of the absorbed flux whose Taylorexpansion agrees with current PN results. This factorized form significantlyimproves the agreement with numerical results obtained with a frequency-domainTeukolsky code, which evolves through a sequence of circular orbits up to thephoton orbit. We perform the comparison between model and numerical data fordimensionless Kerr spins $-0.99 \leq q \leq 0.99$ and for frequencies up to thelight ring of the Kerr black hole. Our proposed model enforces the presence ofa zero in the flux at an orbital frequency equal to the frequency of thehorizon, as predicted by perturbation theory. It also reproduces the expecteddivergence of the flux close to the light ring. Neither of these features arecaptured by the Taylor-expanded PN flux. Our proposed absorption flux can alsohelp improve models for the inspiral, merger, ringdown of small mass-ratiobinary systems.

Modeling the horizon-absorbed gravitational flux for equatorial-circular orbits in Kerr spacetime