Absolute Magnitude Calibration for Red Giants Based on the Colour-Magnitude Diagrams of Galactic Clusters. III. Calibration with 2MASS

We present two absolute magnitude calibrations, M_J and M_{K s}, for red giants with the colour-magnitude diagrams of five Galactic clusters with different metallicities, i.e. M92, M13, M71, M67, and NGC 6791. The combination of the absolute magnitudes of the red giant sequences with the corresponding metallicities provides calibration for absolute magnitude estimation for red giants for a given colour. The calibrations for M_J and M_{K s} are defined in the colour intervals 1.3≤(V-J)₀≤2.8 and 1.75≤(V-K _s)₀≤3.80 mag, respectively, and they cover the metallicity interval -2.15≤[Fe/H]≤+0.37 dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the intervals -0.08<ΔM_J ≤+0.34 and -0.10< Δ M_{K s}≤ +0.27 mag for M_J and M_{K s}, respectively. The means and standard deviations of the residuals are <ΔM_J >=0.137 and σ _{M J} =0.080, and < Δ M_{K s}> =0.109 and σM_{K s}=0.123 mag. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster.