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
"nvσ 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.