Semi-Analytical Model for the Evolution of Stellar Binaries in the Empty Loss Cone of Massive Black Holes
Binary star systems orbiting close to a supermassive black hole (SMBH) evolve through encounters with other stars, the SMBH's tidal forces, and the binary's internal dynamics, including general relativistic precession and tides. Many are driven onto highly eccentric inner binary orbits, potentially leading to stellar mergers; other possible outcomes include hypervelocity star ejections or tidal disruption events. We study the evolution of binaries in the empty loss cone regime, where the outer orbit's angular momentum change per orbit due to scattering off other stars is smaller than the outer angular momentum at the tidal separation radius. We build on the work of Hamers \& Samsing to develop a computationally efficient semi-analytical model that captures the long term evolution of binaries in perturbative regimes where the ratio of the binary tidal separation radius to the pericenter around the SMBH is smaller than 0.15. Crucially, we apply corrections to preserve the orthogonality between the binary's eccentricity and angular momentum vectors, which prevents unphysical eccentricity growth. From these simulations, we find analytical fits for the probability distributions of the final orbital parameters of binaries approaching the SMBH. We find that general relativistic precession efficiently suppresses von-Zeipel-Lidov-Kozai-like eccentricity oscillations and reduces the fraction of merging binaries from $84\%$ with Newtonian physics only, to $3\%$ with precession included. Stellar tides further reduce the merger fraction to $0.4\%$.