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.