Binary dynamics near a massive black hole

We analyze the dynamical evolution of binary stars that interact with a static background of single stars in the environment of a massive black hole (MBH). All stars are considered to be single mass, Newtonian point particles. We follow the evolution of the energy E and angular momentum J of the center of mass of the binaries with respect to the MBH, as well as their internal semi-major axis a, using a Monte Carlo method. For a system like the Galactic center, the main conclusions are the following: (1) The binary fraction can be of the order of a few percent outside 0.1 pc, but decreases quickly closer to the MBH. (2) Within ~0.1 pc, binaries can only exist on eccentric orbits with apocenters much further away from the MBH. (3) Far away from the MBH, loss-cone effects are the dominant mechanism that disrupts binaries with internal velocities close to the velocity dispersion. Closer to the MBH, three-body encounters are more effective in disrupting binaries. (4) The rate at which hard binaries become tighter is usually less than the rate at which a binary diffuses to orbits that are more bound to the MBH. (5) Binaries are typically disrupted before they experience an exchange interaction; as a result, the number of exchanges is less than one would estimate from a simple "nv\sigma estimate''. We give applications of our results to the formation of X-ray binaries near MBHs and to the production rates of hyper-velocity stars by intermediate mass MBHs.