Spin the black circle: horizon absorption on non-circular, planar binary black hole dynamics

Binary systems of black holes emit gravitational waves as they move through their orbits. While most of the emitted radiation escapes to future null infinity, a small fraction is absorbed by the black holes themselves. This is known as horizon absorption or tidal heating/torquing, and causes the black holes' masses and spins to change as the system evolves. In this work, we quantify the effects of the horizon fluxes on binary black hole dynamics by computing them up to next-to-next-to-leading order on generic planar orbits, also exploring physically motivated factorizations of the results. We integrate these fluxes over unbound, hyperbolic-like trajectories obtained with the Effective-One-Body model TEOBResumS-Dal\'i. We discuss the resulting phenomenology across a sizable slice of the relevant parameter space, finding a very small effect in most cases, except on highly energetic orbits. However, the predicted mass and spin variations are quantitatively and qualitatively very sensitive to the analytical representation chosen for the fluxes in that regime. We then perform comparisons with numerical relativity data of induced spins from hyperbolic encounters of initially nonrotating black holes, finding that the next-to-next-to-leading order factorized expressions we derive are crucial to reproduce the data. An optimization on the initial conditions (energy, angular momentum) is necessary for this, however, with differences of up to 9% between the numerical and optimal initial data. Finally, we use our analytical expressions to model possible astrophysical implications for black holes in globular clusters.