The metallicity effect on line-depth ratios in APOGEE $H$-band spectra

Ratios of carefully selected line depths are sensitive to stellar effective temperature ($T_\mathrm{eff}$). Relations established between line-depth ratio (LDR) and $T_\mathrm{eff}$ allow one to determine $T_\mathrm{eff}$ precisely. However, LDRs can also depend on metallicity and abundance ratios, which can limit the accuracy of the LDR method unless such effects are properly taken into account. We investigate the metallicity effect using $H$-band spectra and stellar parameters published by the APOGEE project. We clearly detected the effects of metallicity and abundance ratios; $T_\mathrm{eff}$ derived from a given LDR depends on the metallicity, 100-800$\,$K$\,$dex$^{-1}$, and the dependency on the abundance ratios, 150-1000$\,$K$\,$dex$^{-1}$, also exists when the LDR involves absorption lines of different elements. For the 11 line pairs in the $H$-band we investigated, the LDR-$T_\mathrm{eff}$ relations with abundance-related terms added have scatters as small as 30-90$\,$K within the range of $3700 < T_\mathrm{eff} < 5000$\,K and $-0.7 < \mathrm{[Fe/H]} < +0.4$\,dex. By comparing the observed spectra with synthetic ones, we found that saturation of the absorption lines at least partly explains the metallicity effect.