%astroph/0911.1136

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\begin{document}

\title{Hyper Velocity Stars \\and\\ The Restricted Par=
abolic 3-Body Problem}

\author{Re'em Sari$^{1,2}$, Shiho Kobayashi$^{3,1}$, Elena M. Ross=
i$^1$}

\affil{$^1$Racah Institute of Physics, Hebrew University, =
Jerusalem, Israel, 91904 \\}

\affil{$^2$Theoretical astrophysics =
350-17, California Institute of

=A0=A0 =A0 =A0 =A0 =A0 Technology, Pasadena, CA, 91125 \\}

\=
affil{$^3$Astrophysics Research Institute, Liverpool John Moores University=
, United Kingdom}

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\begin{abstract}

Motivated by detections of hypervelocity st=
ars that may originate from

the Galactic Center, we revist the pr=
oblem of a binary disruption by a

passage near a much more massiv=
e 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<=
/div>

binary-to-black hole mass ratio. Consequently,

an advan=
tage 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 disru=
ption, the lighter star does not remain preferentially

bound to t=
he black hole. In fact, it is ejected exactly in 50\%

of the case=
s. =A0Nonetheless, lighter objects have higher ejection

velocities, since the energy distribution is independent of mass.=A0

Focusing on the planar case,=A0

we provide the probabili=
ty distributions for disruption of circular binaries and for the ejection e=
nergy.

We show that even binaries that penetrate deeply into the tidal

<=
div>sphere of the black hole are not doomed to disruption, but survive in$20\%$ of the cases. Nor do these deep encounters produce the high=
est

ejection energies, which are instead obtained for binaries arriving

--00032557b162185f2104780b9916--
to $0.1-0.5$ of the tidal radius in a prograde orbit. Interestingly=
,

such deep-reaching binaries separate widely after penetrating t=
he 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 s=
ize of

the stars and recast the ejection energy in terms of a min=
imal

possible separation. =A0We find that, for a given minimal separation,<=
/div>

the ejection energy is relatively insensitive to the initial bina=
ry

separation.

\end{abstract}

\keywords{Galaxy: Center, Galaxy: halo, Galaxy: kinematics and

dy=
namics, =A0Galaxy: stellar content, Binaries: general}

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\section{Introduction}

\end{document}