Hyper Velocity Stars and the Restricted Parabolic 3-body Problem
  Motivated by detections of hypervelocity stars that may originate from the
Galactic Center, we revist the problem of a binary disruption by a passage near
a much more massive point mass. The six order of magnitude mass ratio between
the Galactic Center black hole and the binary stars allows us to formulate the
problem in the restricted parabolic three-body approximation. In this
framework, results can be simply rescaled in terms of binary masses, its
initial separation and binary-to-black hole mass ratio. Consequently, an
advantage over the full three-body calculation is that a much smaller set of
simulations is needed to explore the relevant parameter space. Contrary to
previous claims, we show that, upon binary disruption, the lighter star does
not remain preferentially bound to the black hole. In fact, it is ejected
exactly in 50% of the cases. Nonetheless, lighter objects have higher ejection
velocities, since the energy distribution is independent of mass. Focusing on
the planar case, we provide the probability distributions for disruption of
circular binaries and for the ejection energy. We show that even binaries that
penetrate deeply into the tidal sphere of the black hole are not doomed to
disruption, but survive in 20% of the cases. Nor do these deep encounters
produce the highest ejection energies, which are instead obtained for binaries
arriving to 0.1-0.5 of the tidal radius in a prograde orbit. Interestingly,
such deep-reaching binaries separate widely after penetrating the tidal radius,
but always approach each other again on their way out from the black
hole.[shortened]
