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\author{\Huge\bf Krzysztof Z. Stanek}
\affil{\Large Harvard-Smithsonian CfA}
\vspace{-0.6cm}
\author{\Huge\bf Peter M. Garnavich}
\affil{\Large University of Notre Dame}
\vspace{-0.6cm}
\author{\Huge\bf Andrzej Udalski}
\affil{\Large Warsaw University Observatory}


\pagebreak

\vspace*{-2cm}


\begin{center}
{\Huge\bf
\underline{Summary}}
\end{center}

\begin{LARGE}
\begin{bf}

The ideal distance indicator would be a standard candle abundant
enough to provide many examples within reach of parallax measurements
and sufficiently bright to be seen out to Local Group galaxies. As
developed by Paczy\'nski \& Stanek (1998), the red clump method
precisely fits this description.  These stars are the metal rich
equivalent of the better known horizontal branch stars, with weak
metallicity and age brightness dependence.

To date the red clump method has been used to measure accurate
distances to the Galactic center (Paczy\'nski \& Stanek 1998), M31
(Stanek \& Garnavich 1998), LMC (Udalski et al. 1998; Stanek et
al.~1998; Udalski 1999) and some clusters in our Galaxy (e.g. 47Tuc:
Kaluzny et al. 1998). As with all the distance indicators, the main
worry lies in the possible systematics of the method, in this case its
dependence on the stellar metallicity and age.  Both of these
dependences were investigated by Udalski (1998a) and Udalski
(1998b). More recently, the metallicity dependence of the red clump
brightness was investigated by Stanek et al.~(1999), Udalski (1999)
and Popowski (1999). So far all these studies indicate that indeed the
population effects on the red clump brightness are small. We discuss
further planned studies of the red clump properties.

Perhaps the most important result from the red clump method was the
determination of the ``short'' distance to the Large Magellanic Cloud
(Udalski et al. 1998; Stanek, Zaritsky \& Harris 1998; Udalski
1999). If accurate, this distance to the LMC shorter by 12\% than the
``standard'' value, has very important implications for the Cepheid
distance scale and the determination of the Hubble constant.

\end{bf}
\end{LARGE}

\pagebreak

\noindent
\rule{7.5in}{2mm}
\begin{center}
{\huge\bf\underline{Hipparcos calibration of the red clump}}
\end{center}

\begin{LARGE}
\begin{bf}

The {\em Hipparcos}\/ based absolute magnitude-color diagram is shown
in the central figure, for the stars with parallaxes measured to
better than 10\%.  There are about 600 such stars within the
rectangular region.  Stanek \& Garnavich (1998) selected a sub-sample
of 228 {\em Hipparcos}\/ red clump stars with the distance $d<70\;pc$
and parallaxes measured to better than 5\%, and they determined the
parameters of the best fit to the luminosity function:
$M_{I,m}(d<70\;pc) = -0.227 \pm 0.023$, and $\sigma_{RC}=0.209$ mag
for these nearby stars, with the average distance $\langle
d_{<70}\rangle =50\;pc$.  One expects very little reddening,
$E(B-V)<0.02$, for such nearby stars, so they assumed that their
$d<70\;pc$ sample suffered no reddening.

\end{bf}
\end{LARGE}


\pagebreak

\begin{center}
{\huge\bf\underline{Systematics of the red clump method}}
\end{center}

\begin{LARGE}
\begin{bf}

As with all the distance indicators, the main worry lies in the
possible systematics of the red clump method, in this case its
dependence on the stellar metallicity and age.  We are investigating
these systematic effects using samples of globular clusters observed
in M31 and M33 with the HST.  The fact that the derived distance
moduli for the three fields in M31 used by Stanek \& Garnavich (1998)
vary by only $0.035\;$mag indicates that indeed the population effects
on the red clump brightness are small. The age dependence was
investigated by Udalski (1998b) and found to be small, using large
samples of red clump stars collected by the OGLE collaboration in the
LMC and the SMC (Fig.~1).

\pagebreak

The metallicity dependence of the red clump was first investigated by
Udalski (1998b) and more recently by Udalski (1999).  Using nearby
bright stars with well measured {\em Hipparcos} parallaxes and high
quality spectroscopy, he found a weak metallicity dependence of
$0.13\;mag\;dex^{-1}$ for the red clump $I$-band peak brightness
(Fig.~2).  The metallicity dependence was also investigated by Stanek
et al.~(1999) using Galactic bulge stars observed in Baade's Window
(Fig.~3). These empirical determinations are in a very good agreement
with recent models of stellar evolution (e.g. Girardi 1999).

\end{bf}
\end{LARGE}

\pagebreak

\noindent
\rule{7.5in}{2mm}
\begin{center}
{\Huge\bf\underline{Red clump distance to the LMC}}
\end{center}

\begin{LARGE}
\begin{bf}

Udalski et al.~(1998) and Stanek, Zaritsky \& Harris (1998) derived
the distance to the Large Magellanic Cloud by comparing red clump
stars from the {\em Hipparcos}\/ catalog with the red clump stars
observed in several fields in the LMC.  They obtained a single step
determination of the distance modulus to the LMC, $\mu_{0,LMC} =
18.08\pm 0.03\pm 0.12\;$mag (statistical plus systematic error)
(Udalski et al.~1998) and $\mu_{0,LMC} = 18.065\pm 0.031\pm 0.09\;$mag
(Stanek et al.~1998). These studies assumed the red clump to be a
perfect standard candle whose brightness does not depend on population
effects.

The most recent value of the red clump distance to the LMC was
obtained by Udalski (1999): $\mu_{0,LMC} = 18.24\pm 0.08\;$mag, a
value $\sim 0.25\;$mag smaller than the generally accepted value of
$\mu_{0,LMC} = 18.50\pm 0.10\;$mag. This study used very
low-extinction fields in the LMC and the metallicity dependence of
$0.13\;mag\;dex^{-1}$, discussed elsewhere in this poster.  The value
obtained by Udalski (1999) is free of zero-point calibration problems,
reddening uncertainties and is corrected for population effects, thus
representing the most robust LMC distance estimate available to date.


\end{bf}
\end{LARGE}

\pagebreak


\begin{large}
\begin{bf}

\begin{center}
{\Large ~~~~~~Distance moduli with the red clump}
\end{center}
\vspace{-0.55cm}

\begin{tabular}{cccccc}
\hline
\hline
47 Tuc & GB  & LMC  & SMC & Carina DG & M31 \\
\hline
$13.38\pm 0.05$ &  $14.53\pm 0.06$ & $18.24\pm 0.08$ & $18.73\pm 0.10$ &
$19.84 \pm 0.07$ & $24.51\pm 0.07$ \\ 
\hline
\hline

\end{tabular}


\end{bf}
\end{large}

\pagebreak

\begin{figure}[t]
\plotfiddle{dummy.ps}{16cm}{0}{80}{80}{-250}{-100}
\caption{Mean $I$-band brightness of the red clump as a function of
age for the LMC and SMC. Filled dots represent clusters of
intermediate age (2--10 Gyr) while asterisks represent older
clusters (from Udalski 1998b).}
\end{figure}

\pagebreak

\begin{figure}[t]
\plotfiddle{dummy.ps}{16cm}{0}{80}{80}{-250}{-125}
\caption{$M_I$ of 284 nearby red giants with precise photometry and
spectroscopy plotted as a function of color $V-I$ (left panel) and
metallicity $[Fe/H]$ (right panel). Stars of low, medium and high
metallicity are marked by filled circles, filled triangles and open
circles, respectively (from Udalski 1999).}
\end{figure}

\pagebreak


\begin{figure}[t]
\plotfiddle{dummy.ps}{16cm}{0}{80}{80}{-250}{-100}
\caption{$M_I$ absolute magnitude - dereddened color diagrams for the
BW8 field. Also plotted are the $t=10\;Gy$ isochrones and the the
dereddened maximum density ridge-lines for 47Tuc ($[Fe/H]\approx
-0.7$: triangles) and NGC6791 ($[Fe/H]\approx +0.3$: circles)
(from Stanek et al.~1999).}
\end{figure}

\end{document}
