Hypervelocity stars and the restricted parabolic three-body problem

Motivated by detections of hypervelocity stars that may originate from the Galactic center, we revisit the problem of a binary disruption by a passage near a much more massive point mass. The six orders of magnitude mass ratio between the Galactic center black hole (BH) 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, their initial separation, and the 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 in exactly 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 BH 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 BH. Finally, our analytic method allows us to account for a finite size of the stars and recast the ejection energy in terms of a minimal possible separation. We find that, for a given minimal separation, the ejection energy is relatively insensitive to the initial binary separation.