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\title{The distribution of stars near the super-massive black hole in the Galactic
Center}

\author{Tal Alexander}

\maketitle
\affil{Institute for Advanced Study, Olden Lane, Princeton, NJ 08540} 

\authoremail{tal@ias.edu}

\begin{abstract}
We analyze three sets of infrared star counts in the inner ~0.5 pc of
the Galactic Center. We perform statistical tests on the star counts
and model in detail the extinction field and the effects of
dwarf-giant collisions on the luminosity function. We find that both
the star counts and the depletion of the brightest stars in the inner
~0.05 pc can be explained by a r^-\alpha stellar cusp with \alpha in
the range 3/2 to 7/4, in which the envelopes of the brightest giants
are destroyed by stellar collisions. Such a cusp is consistent with
the Bahcall-Wolf solution for the distribution of stars that have
undergone two-body relaxation around a black hole. We show that
systematic uncertainties due to variable extinction and unrelaxed
stars are probably small, but deeper star counts are required to
confirm these results. We estimate that the tidal disruption rate of
cusp stars by the black hole is few x 10^-5 yr^-1.
\end{abstract}