Photometric Calibration of the [$α$/Fe] Element: I. Calibration with UBV Photometry

Abstract: We present the calibration of the [$\alpha$/Fe] element in terms of the ultra-violet excess for 469 dwarf stars with $0.325<(B-V)_0 \leq 0.775$ mag corresponding 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 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 a good agreement between the distribution of the synthetic alpha elements versus ultra-violet excesses and the ones obtained via our calibrations.