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We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.

As active galactic nuclei (AGN) `turn on', some stars end up embedded in accretion disks around supermassive black holes (SMBHs) on retrograde orbits. Such stars experience strong headwinds, aerodynamic drag, ablation and orbital evolution on short timescales. Loss of orbital angular momentum in the first $\sim 0.1$~Myr of an AGN leads to a heavy rain of stars (`starfall') into the inner disk and onto the SMBH. A large AGN loss cone ($\theta_{\rm AGN,lc}$) can result from binary scatterings in the inner disk and yield tidal disruption events (TDEs). Signatures of starfall include optical/UV flares that rise in luminosity over time, particularly in the inner disk. If the SMBH mass is $M_{\rm SMBH} \ge 10^{8}M_{\odot}$, flares truncate abruptly and the star is swallowed. If $M_{\rm SMBH}, Comment: 10 pages, 1 figure, MNRAS submitted