# Hyper Velocity Stars and The Restricted Parabolic 3-Body Problem

## Re'em Sari^{1,2}, Shiho Kobayashi^{3,1}, Elena M. Rossi^{1}

(1) Racah Institute of Physics, Hebrew University, Jerusalem, Israel, 91904

(2) Theoretical astrophysics 350-17, California Institute of Technology, Pasadena, CA, 91125

(3) Astrophysics Research Institute, Liverpool John Moores University, United Kingdom

### Paper: 2009, ApJ, accepted

**Abstract:**
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.
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.

Preprints available from the authors at issor.em@gmail.com
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