Absolute Magnitude Calibration for Red Clump Stars
  We combined the ($K_s$, $J-K_s$) data in Laney et al. (2012) with the $V$
apparent magnitudes and trigonometric parallaxes taken from the Hipparcos
catalogue and used them to fit the $M_{K_s}$ absolute magnitude to a linear
polynomial in terms of $V-K_s$ colour. The mean and standard deviation of the
absolute magnitude residuals, -0.001 and 0.195 mag, respectively, estimated for
224 red clump stars in Laney et al. 2012 are (absolutely) smaller than the
corresponding ones estimated by the procedure which adopts a mean
$M_{K_s}=-1.613$ mag absolute magnitude for all red clump stars, -0.053 and
0.218 mag, respectively. The statistics estimated by applying the linear
equation to the data of 282 red clump stars in Alves (2000) are larger, $\Delta
M_{K_s}=0.209$ and $\sigma=0.524$ mag, which can be explained by a different
absolute magnitude trend, i.e. condensation along a horizontal distribution.
