Ejection and Capture Dynamics in Restricted Three-Body Encounters
  We study the tidal disruption of binaries by a massive point mass (e.g. the
black hole at the Galactic center), and we discuss how the ejection and capture
preference between unequal-mass binary members depends on which orbit they
approach the massive object. We show that the restricted three-body
approximation provides a simple and clear description of the dynamics. The
orbit of a binary with mass m around a massive object M should be almost
parabolic with an eccentricity |1-e| < (m/M)^{1/3} << 1 for a member to be
captured, while the other is ejected. Indeed, the energy change of the members
obtained for a parabolic orbit can be used to describe non-parabolic cases. If
a binary has an encounter velocity much larger than (M/m)^{1/3} times the
binary rotation velocity, it would be abruptly disrupted, and the energy change
at the encounter can be evaluated in a simple disruption model. We evaluate the
probability distributions for the ejection and capture of circular binary
members and for the final energies. In principle, for any hyperbolic (elliptic)
orbit, the heavier member has more chance to be ejected (captured), because it
carries a larger fraction of the orbital energy. However, if the orbital energy
is close to zero, the difference between the two members becomes small, and
there is practically no ejection and capture preference. The preference becomes
significant when the orbital energy is comparable to the typical energy change
at the encounter. We discuss its implications to hypervelocity stars and
irregular satellites around giant planets.
