Formation of Close Binaries through Massive Black Hole Perturbations and Chaotic Tides

Hills breakup of binary systems allows massive black holes (MBH) to produce hyper-velocity stars (HVSs) and tightly bound stars. The long timescale of orbital relaxation means that binaries must spend numerous orbits around the MBH before they are tidally broken apart. Repeated MBH tidal perturbations over multiple pericenter passages can perturb the binary inner orbit to high eccentricities, leading to strong tidal interactions between the stars. In this work, we develop a physical model of the MBH-binary system, taking into account outer orbital relaxation, MBH tidal perturbations, and tidal interactions between the binaries in the form of dynamical tides. We show that when the inner orbit reaches high eccentricities such that the pericenter radius is only a few times stellar radii (\(R_*\)), the stellar oscillation modes can grow chaotically and rapidly harden the binaries to semi-major axes \(a_b\lesssim 10\,R_*\). We find that a significant fraction (up to 50%) of initially wide binaries that are in the empty loss-cone regime (\(a_b\sim 1.0\,{\rm AU}\)) do not undergo Hills breakup as wide binaries, but instead experience chaotic growth of tides and become close binaries. These tidally hardened binaries provide a new channel for the production of the fastest HVSs, and are connected to other nuclear transients such as repeating partial tidal disruption events and quasi-periodic eruptions.