A metallicity scale derived from Fe I and FeH lines in the APOGEE M dwarf spectra

We present metallicities derived from a sample of eleven M dwarfs belonging to wide binary systems with warmer FG primary companions observed by the high-resolution (R=22,500) near-infrared SDSS-IV APOGEE spectra. Using a plane-parallel one-dimensional local thermodynamic equilibrium (LTE) abundance analysis, we determine effective temperatures ($T_{\rm eff}$) based on the abundance equilibrium from the Fe I, FeH, OH, and H$_2$O spectral lines. We obtained three $T_{\rm eff}$ scales based on these lines and found that, regardless of the chosen $T_{\rm eff}$ scale, the M dwarf metallicities agree well with those of the warmer primaries, where the upper mean abundance difference limit is 0.04 $\pm$ 0.06. This good agreement confirms that FeH lines are a reliable indicator of $T_{\rm eff}$ in the $H-$band spectra.