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%astroph/0911.1136


\documentclass[]{emulateapj}

\def\ltsima{$\; \buildrel < \over \sim \;$}
\def\lsim{\lower.5ex\hbox{\ltsima}}
\def\gtsima{$\; \buildrel > \over \sim \;$}
\def\gsim{\lower.5ex\hbox{\gtsima}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\no{\noindent}
\renewcommand{\vec}[1]{{\bf #1}}
\newcommand{\bhat}[1]{{\hat {\bf #1}}}
\newcommand{\greekvec}[1]{\mbox{\boldmath{$#1$}}}

\begin{document}

\title{Hyper Velocity Stars \\and\\ The Restricted Parabolic 3-Body Problem}
\author{Re'em Sari$^{1,2}$, Shiho Kobayashi$^{3,1}$, Elena M. Rossi$^1$}
\affil{$^1$Racah Institute of Physics, Hebrew University, Jerusalem, Israel,
91904 \\}
\affil{$^2$Theoretical astrophysics 350-17, California Institute of
           Technology, Pasadena, CA, 91125 \\}
\affil{$^3$Astrophysics Research Institute, Liverpool John Moores
University, United Kingdom}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{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.

\end{abstract}
\keywords{Galaxy: Center, Galaxy: halo, Galaxy: kinematics and
dynamics,  Galaxy: stellar content, Binaries: general}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}





\end{document}

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Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div><br></div><div>%astroph/0911.1136</div><div><br></div=
><div><br></div><div>\documentclass[]{emulateapj}</div><div><br></div><div>=
\def\ltsima{$\; \buildrel &lt; \over \sim \;$}</div><div>\def\lsim{\lower.5=
ex\hbox{\ltsima}}</div>
<div>\def\gtsima{$\; \buildrel &gt; \over \sim \;$}</div><div>\def\gsim{\lo=
wer.5ex\hbox{\gtsima}}</div><div>\def\be{\begin{equation}}</div><div>\def\e=
e{\end{equation}}</div><div>\def\no{\noindent}</div><div>\renewcommand{\vec=
}[1]{{\bf #1}}</div>
<div>\newcommand{\bhat}[1]{{\hat {\bf #1}}}</div><div>\newcommand{\greekvec=
}[1]{\mbox{\boldmath{$#1$}}}</div><div><br></div><div>\begin{document}</div=
><div><br></div><div>\title{Hyper Velocity Stars \\and\\ The Restricted Par=
abolic 3-Body Problem}</div>
<div>\author{Re&#39;em Sari$^{1,2}$, Shiho Kobayashi$^{3,1}$, Elena M. Ross=
i$^1$}</div><div>\affil{$^1$Racah Institute of Physics, Hebrew University, =
Jerusalem, Israel, 91904 \\}</div><div>\affil{$^2$Theoretical astrophysics =
350-17, California Institute of</div>
<div>=A0=A0 =A0 =A0 =A0 =A0 Technology, Pasadena, CA, 91125 \\}</div><div>\=
affil{$^3$Astrophysics Research Institute, Liverpool John Moores University=
, United Kingdom}</div><div><br></div><div>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%=
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</div>
<div>\begin{abstract}</div><div>Motivated by detections of hypervelocity st=
ars that may originate from</div><div>the Galactic Center, we revist the pr=
oblem of a binary disruption by a</div><div>passage near a much more massiv=
e point mass. The six order of</div>
<div>magnitude mass ratio between the Galactic Center black hole and the</d=
iv><div>binary stars allows us to formulate the problem in the restricted</=
div><div>parabolic three-body approximation. In this framework, results can=
 be</div>
<div>simply rescaled in terms of binary masses, its initial separation and<=
/div><div>binary-to-black hole mass ratio. Consequently,</div><div>an advan=
tage over the full three-body calculation is that</div><div>a much smaller =
set of simulations is needed to explore the relevant parameter space.</div>
<div>Contrary to previous claims, we show that, upon</div><div>binary disru=
ption, the lighter star does not remain preferentially</div><div>bound to t=
he black hole. In fact, it is ejected exactly in 50\%</div><div>of the case=
s. =A0Nonetheless, lighter objects have higher ejection</div>
<div>velocities, since the energy distribution is independent of mass.=A0</=
div><div>Focusing on the planar case,=A0</div><div>we provide the probabili=
ty distributions for disruption of circular binaries and for the ejection e=
nergy.</div>
<div>We show that even binaries that penetrate deeply into the tidal</div><=
div>sphere of the black hole are not doomed to disruption, but survive in</=
div><div>$20\%$ of the cases. Nor do these deep encounters produce the high=
est</div>
<div>ejection energies, which are instead obtained for binaries arriving</d=
iv><div>to $0.1-0.5$ of the tidal radius in a prograde orbit. Interestingly=
,</div><div>such deep-reaching binaries separate widely after penetrating t=
he tidal radius, but</div>
<div>always approach each other again on their way out from the black hole.=
</div><div>Finally, our analytic method allows us to account for a finite s=
ize of</div><div>the stars and recast the ejection energy in terms of a min=
imal</div>
<div>possible separation. =A0We find that, for a given minimal separation,<=
/div><div>the ejection energy is relatively insensitive to the initial bina=
ry</div><div>separation.</div><div><br></div><div>\end{abstract}</div><div>
\keywords{Galaxy: Center, Galaxy: halo, Galaxy: kinematics and</div><div>dy=
namics, =A0Galaxy: stellar content, Binaries: general}</div><div>%%%%%%%%%%=
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</div><div>
\section{Introduction}</div><div><br></div><div><br></div><div><br></div><d=
iv><br></div><div><br></div><div>\end{document}</div>
</div>

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