The Distances to Open Clusters from Main-Sequence Fitting. V. Extension
  of Color Calibration and Test using Cool and Metal-Rich Stars in NGC 6791
  We extend our effort to calibrate stellar isochrones in the Johnson-Cousins
($BVI_C$) and the 2MASS ($JHK_s$) filter systems based on observations of
well-studied open clusters. Using cool main-sequence (MS) stars in Praesepe, we
define empirical corrections to the Lejeune et al. color-effective temperature
($T_{\rm eff}$) relations down to $T_{\rm eff} \sim 3600$ K, complementing our
previous work based on the Hyades and the Pleiades. We apply empirically
corrected isochrones to existing optical and near-infrared photometry of cool
($T_{\rm eff} \leq 5500$ K) and metal-rich ([Fe/H]$=+0.37$) MS stars in NGC
6791. The current methodology relies on an assumption that color-$T_{\rm eff}$
corrections are independent of metallicity, but we find that estimates of
color-excess and distance from color-magnitude diagrams with different color
indices converge on each other at the precisely known metallicity of the
cluster. Along with a satisfactory agreement with eclipsing binary data in the
cluster, we view the improved internal consistency as a validation of our
calibrated isochrones at super-solar metallicities. For very cool stars
($T_{\rm eff} \leq 4800$ K), however, we find that $B - V$ colors of our models
are systematically redder than the cluster photometry by $\sim0.02$ mag. We use
color-$T_{\rm eff}$ transformations from the infrared flux method (IRFM) and
alternative photometry to examine a potential color-scale error in the input
cluster photometry. After excluding $B - V$ photometry of these cool MS stars,
we derive $E(B - V)=0.105\pm0.014$, [M/H]$=+0.42\pm0.07$, $(m - M)_0 =
13.04\pm0.08$, and the age of $9.5\pm0.3$ Gyr for NGC 6791.
