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%astro-ph/0402338
%http://hera.ph1.uni-koeln.de/~nelly/Mouawad-CuspGC.ps

||\documentstyle{article}
\begin{document}

\title{Weighing the cusp at the Galactic Centre}


  \author{N. Mouawad
          \inst{1}
          \and
          A. Eckart\inst{1}
          \and
          S. Pfalzner\inst{1}
          \and
          R. Sch\"odel\inst{1}
          \and
          J. Moultaka\inst{1}
          \and
          R. Spurzem\inst{2}
         }

   \institute{I. Physikalisches Institut, Universit\"at zu K\"oln,
               Z\"ulpicher Str.77, 50937 K\"oln, Germany
    \and              Astronomisches Recheninstitut, M\"onchhofstr. 
12-14, 69120 Heidelberg, Germany
             }

\date{Received $<$date$>$;
accepted $<$date$>$;
published online $<$date$>$}

\abstract{As stars close to the galactic centre have short orbital
periods it has been possible to trace large
fractions of their orbits in the recent years.
Previously the data of the orbit of the star S2 have
been fitted with Keplerian orbits corresponding to a
massive black hole (MBH)
with a mass of M$_{BH}$=3-4$\times$10$^6$M$_{\odot}$
implying an insignificant cusp mass.
However, it
has also been shown that the central black hole resides in a $\sim$1''
diameter stellar cluster of a priori unknown mass.  In a
spherical potential which is neither Keplerian nor harmonic, orbits
will precess resulting in inclined rosetta shaped trajectories on the
sky.  In this case, the assumption of non-Keplerian orbits is a more
physical approach.  It is also the only approach through which cusp
mass information can be obtained via stellar dynamics of the cusp
members.  This paper presents the first exemplary modelling efforts in
this direction.
Using positional and radial data of star S2, we find that there could exist
an unobserved extended mass component of
several 10$^5$M$_{\odot}$ forming a so-called 'cusp'
centered on the black hole position.
Considering only the fraction of the cusp mass M$_{S2_{apo}}$ within the
apo-center of the S2 orbit we find as an upper limit that
M$_{S2_{apo}}$/(M$_{BH}$ + M$_{S2_{apo}}$) $\le$ 0.05.

A large extended cusp mass, if present, is unlikely
to be composed of sub-solar mass constituents, but could be
explained rather well by a cluster of high M/L stellar remnants,
which we find to form a stable configuration.}
\end{document}