Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation

We propose, within the effective one body (EOB) approach, a new, resummed, analytical representation of the gravitational wave energy flux absorbed by a system of two circularized (nonspinning) black holes. This expression is such to be well-behaved in the strong-field, fast motion regime, notably up to the EOB-defined last unstable orbit. Building conceptually upon the procedure adopted to resum the multipolar asymptotic energy flux, we introduce a {\it multiplicative} decomposition of the multipolar absorbed flux made by three factors: (i) the leading-order contribution, (ii) an "effective source" and (iii) a new residual amplitude correction $(\tilde{\rho}_\lm^H)^{2\ell}$. In the test-mass limit, we use a frequency-domain perturbative approach to accurately compute numerically the horizon-absorbed fluxes along a sequence of stable and unstable circular orbits and we extract from them the functions $\tilde{\rho}_\lm^H$. These quantities are then fitted via rational functions. The resulting analytically represented test-mass knowledge is then suitably {\it hybridized} with lower-order analytical information that is valid for any mass ratio. This yields a resummed representation of the absorbed flux for a generic, circularized, nonspinning black-hole binary. Our result adds new information to the state-of-the-art calculation of the absorbed flux at fractional 5 post-Newtonian order [S. Taylor and E. Poisson, Phys. Rev. D {\bf 78} 084016 (2008)], that is recovered in the weak-field limit approximation by construction.