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 $1.3\leq(V-J)_{0}\leq2.8$ and $1.75 \leq (V-K_{s})_{0}\leq 3.80$ mag, respectively, and they cover 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 intervals $-0.08<\Delta M_{J}\leq +0.34$ and $-0.10< \Delta M_{K_s}\leq +0.27$ mag for $M_{J}$ and $M_{K_s}$, respectively. The means and standard deviations of the residuals are $= 0.137$ and $\sigma_{M_J}=0.080$, and $=0.109$ and $\sigma_{M_{K_{s}}}=0.123$ mag. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster.Comment: 20 pages, including 8 figures and 22 tables, accepted for publication in PASA. arXiv admin note: substantial text overlap with arXiv:1206.275

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

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 $\leq(g-r)_{0}\leq$ 1.30 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 $-0.28< \Delta M \leq +0.43$ mag. However, the range of 94% of the residuals is shorter, $-0.1<\Delta M \leq+0.4$ 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.Comment: 12 pages, including 5 figures and 10 tables, accepted for publication in PASA. arXiv admin note: substantial text overlap with arXiv:1204.429

Photometric calibration of the [alpha/Fe] element: I. Calibration with U BV photometry

We present the calibration of the [alpha/Fe] element in terms of the ultra-violet excess for 469 dwarf stars with 0.325 < (B -V)(0) <= 0.775 mag corresponding to the spectral type range F0-K2. The star sample is separated into nine sub-samples with equal range in (B -V)(0) colour, Delta(B-V)(0) = 0.05 mag, and a third degree polynomial is fitted to each dataset. Our calibrations provide [alpha/Fe] elements in the range [0.0, 0.4]. We applied the procedure to two sets of field stars and two sets of clusters. The mean and the corresponding standard deviation of the residuals for 43 field stars taken from the Hypatia catalogue are [alpha/Fe] = -0.090 and sigma = 0.102 dex, while for the 39 ones taken from the same catalogue of stars used in the calibration these quantities are [alpha/Fe] = -0.009 and sigma = 0.079 dex, respectively. We showed that the differences between the mean of the residuals and standard deviations for two sets of clusters ([alpha/Fe] = 0.073 and sigma = 0.91 dex; [alpha/Fe] = -0.012 and sigma = 0.053 dex) originate from the (B - V)(0) and (U - B)(0) colour indices of the clusters which are taken from different sources. The differences between the original [alpha/Fe] elements and the estimated ones (the residuals) are compatible with the uncertainties in the literature. Also, there is good agreement between the distribution of the synthetic alpha elements versus ultra-violet excesses and the ones obtained via our calibrations