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Absolute Magnitude Calibration for Dwarfs Based on the Colour-Magnitude Diagrams of Galactic Clusters

We present two absolute magnitude calibrations for dwarfs based on colour-magnitude diagrams of Galactic clusters. The combination of the $M_g$ absolute magnitudes of the dwarf fiducial sequences of the clusters M92, M13, M5, NGC 2420, M67 and NGC 6791 with the corresponding metallicities provides absolute magnitude calibration for a given $(g-r)_0$ colour. The calibration is defined in the colour interval $0.25\leq (g-r)_0 \leq 1.25$ mag and it covers the metallicity interval $-2.15\leq \lbrack Fe/H\rbrack \leq +0.37$ dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the interval $-0.15 \leq ΔM_g \leq +0.12$ mag. The mean and standard deviation of the residuals are $<ΔM_g>=-0.002$ and $σ=0.065$ mag, respectively. The calibration of the $M_J$ absolute magnitude in terms of metallicity is carried out by using the fiducial sequences of the clusters M92, M13, 47 Tuc, NGC 2158 and NGC 6791. It is defined in the colour interval $0.90 \leq (V-J)_0 \leq 1.75$ mag and it covers the same metallicity interval of the $M_g$ calibration. The absolute magnitude residuals obtained by the application of the procedure to the cluster M5 ($\lbrack Fe/H\rbrack=-1.40$ dex) and 46 solar metallicity, $-0.45 \leq \lbrack Fe/H\rbrack \leq +0.35$ dex, field stars lie in the interval -0.29 and +0.35 mag. However, the range of 87 per cent of them is rather shorter, $-0.2 \leq ΔM_J \leq +0.2$ mag. The mean and standard deviation of all residuals are $<ΔM_J>=0.05$ and $σ$=0.13 mag, respectively. The derived relations are applicable to stars older than 4 Gyr for the $M_g$ calibration, and older than 2 Gyr for the $M_J$ calibration. The cited limits are the ages of the youngest calibration clusters in the two systems.