Absolute Magnitude Calibration for Giants Based on the Colour–Magnitude Diagrams of Galactic Clusters. II. Calibration with SDSS

Abstract

We present an absolute magnitude calibration for red giants with the colour-magnitude diagrams of six Galactic clusters with different metallicities, i.e. M92, M13, M3, M71, NGC 6791, and NGC 2158. 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 (g − r) 0 colour. The calibration is defined in the colour interval 0.45 ࣘ (g − r) 0 ࣘ 1.30 mag and it covers 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 interval −0.28 < M ࣘ +0.43 mag. However, the range of 94% of the residuals is shorter, −0.1 < M ࣘ +0.4 mag. The mean and the standard deviation of (all) residuals are 0.169 and 0.140 mag, respectively. The derived relations are applicable to stars older than 2 Gyr, the age of the youngest calibrating cluster.

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

“…The residuals lie between −0.15 and +0.12 mag, and their mean and standard deviations are < M >= −0.002 and σ = 0.065 mag. The range of the residuals estimated for the red giants with SDSS was −0.28 ≤ M ≤ +0.43 mag (Karaali et al 2013a), larger than the one for the dwarfs estimated in this study. Also, their mean and standard deviation were larger, i.e.…”

“…However, we note that the dwarf sequence is not steep. Hence, contrary to the red giant branch sequence Karaali et al (2013a), an error in (g − r) or (V − J) does not imply a large change in the absolute magnitude. The c i and d i (i = 0, 1, 2) coefficients in Tables 9 and 12, respectively, are colour-dependent.…”

“…Thus, the absolute magnitude M J of a dwarf would be determined with an accuracy of M < 0.2 mag. The mean and standard deviation of the residuals estimated with the same photometry (V, J) for red giants were < M >= 0.137 and σ = 0.080 mag (Karaali et al 2013b) which indicates that the absolute magnitudes of dwarfs would be determined with better accuracy. The reason of this improvement is the same as stated for the absolute magnitude M g .…”

“…We adopted the procedure used in our previous papers (Karaali et al 2013a(Karaali et al , 2013b) which consists of calibration of an absolute magnitude as a function of metallicity. We calibrated the M g and M J absolute magnitudes in terms of metallicity for a given (g − r) 0 and (V − J) 0 colour, respectively.…”

“…The most recent absolute magnitude calibrations are those of Karaali, Bilir, & Yaz Gökçe (2012) and Karaali, Bilir & Yaz Gökçe (2013a, 2013b. Karaali et al combined the colour-apparent magnitude diagrams of Galactic clusters with different metal abundances and their distance moduli, and calibrated the M V , M g , M J , and M K s absolute magnitudes of red giants in terms of metallicity.…”