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From: Vernon Bailey  vbailey@ast.cam.ac.uk 
X-Sender: vbailey@cass20
To: Galactic Center Newsletter <gcnews@aoc.nrao.edu>
Subject:Red giant collisions in the galactic centre astro-ph/9907309
MIME-Version: 1.0

%astro-ph/9907309
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\def\cf{{\it cf.\ }}
\def\eg{{\it e.g.\ }}
\def\ie{{\it i.e.\ }}
\def\vinf{V_\infty}
\def\rmin{R_{\rm min}}
\def\deltam{\Delta M\,}
\def\deltaee{\Delta E/E\,}
\def\etal{{\it et al.\ }}
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\def\AK{A$_{\rm K}$}

\title{Red giant collisions in the galactic centre}
\author{V. C. Bailey, M. B. Davies}

\begin{abstract}

We simulate collisions involving red-giant stars in the centre of our
galaxy. Such encounters may explain the observed paucity of highly
luminous red giants within $\sim 0.2\,$pc of Sgr A$^\star$. The masses of
the missing stars are likely to be in the range $\sim 2\,$M$_\odot\,-\,8
\,$M$_\odot$. 
Recent models of the galactic centre cluster's 
density distribution and velocity dispersion
are used to calculate two-body collision rates. 
In particular we use stellar-evolution models to calculate
the number of collisions a star will have during different 
evolutionary phases. We find that the number of two-body 
collisions per star is $\lo 1$ in the central $0.1\,$pc$\,-\,0.2\,$pc, 
depending strongly on the galactocentric radius, with some
uncertainty from the assumed cluster models and stellar-evolution
models. Using a 3D numerical hydrodynamics code (SPH) we simulate
encounters involving cluster stars of various masses with a $2\,$M$_\odot$
red giant and an $8\,$M$_\odot$ red giant. The instantaneous mass loss in such
collisions is rarely enough to destroy either giant. A fraction of
the collisions do, however, lead to the formation of common envelope
systems where the impactor and giant's core are enshrouded by the
envelope of the giant. Such
systems may evolve to expel the envelope, leaving a tight binary; the
original giant is destroyed. 
The fraction of collisions that produce common envelope
systems is sensitive to the local velocity dispersion and hence
galactocentric radius. Whereas most of our collisions lead to common envelope
formation at a few parsecs from Sgr A$^\star$, very few collisions do
so within the central $0.2\,$pc. Using our collision-rate calculations we then 
compute
the time-scales for a giant star to suffer such a collision within the
galactic centre. These time-scales are $\go 10^{9-10}$ years and so
are longer than the lifetimes of stars more-massive than $\sim
2\,$M$_\odot$. Thus the observed paucity of luminous giants is unlikely to be
due to the formation of common envelope systems as a result of
two-body encounters involving giant stars. 
\end{abstract}



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