$H$-band Temperature and Metallicity Indicators for Cool Giants: Empirical Relations in Bayesian Framework

Abstract

We explored here the near-infrared $H$-band atmospheric window aiming to provide quantitative diagnostic tools for deriving stellar parameters, for instance, effective temperature ($T_{eff}$) and metallicity ([$Fe/H$]), of cool giants ($T_{eff}$ $<$ 5000 K) using low-resolution spectra. We obtained 177 cool giants from the X-shooter spectral library covering a wider metallicity range ($-$2.35 dex $<$ [$Fe/H$] $<$ 0.5 dex) than in earlier works. Degrading the spectral resolution to R$\sim$ 1200, we estimated equivalent widths of several important spectral features, and the behavior of spectral features with stellar parameters are studied. Also, the empirical relations for deriving $T_{eff}$ and [$Fe/H$] are established in the Bayesian framework. We found that ${}^{12}$CO at 1.56 $\mu$m and 1.62 $\mu$m, and ${}^{12}$CO+MgI at 1.71 $\mu$m are the best three $T_{eff}$ indicators with a typical accuracy of 153 K, 123 K and 107 K, respectively. The cubic Bayesian model provides the best metallicity estimator with a typical accuracy of 0.22 dex, 0.28 dex, and 0.24 dex for FeH at 1.62 $\mu$m, ${}^{12}$CO at 1.64 $\mu$m, and Fe I at 1.66 $\mu$m, respectively. We also showed a detailed quantitative metallicity dependence of $T_{eff}-$EWs correlations defining three metallicity groups, supersolar ([$Fe/H$] $>$ 0.0 dex), solar ($-$0.3 dex $<$ [$Fe/H$] $<$ 0.3 dex), and subsolar ([$Fe/H$] $<$ $-$0.3 dex), from Hierarchical Bayesian modelling. The difference between the solar and subsolar relationship is statistically significant, but such difference is not evident between the solar and supersolar groups.

arXiv comment15 pages, 16 figures, 5 tables. Accepted for publication in MNRAS

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