Chemical Abundances of M-dwarfs from the APOGEE Survey. I. The Exoplanet
  Hosting Stars Kepler-138 and Kepler-186
  We report the first detailed chemical abundance analysis of the
exoplanet-hosting M-dwarf stars Kepler-138 and Kepler-186 from the analysis of
high-resolution ($R$ $\sim$ 22,500) $H$-band spectra from the SDSS IV - APOGEE
survey. Chemical abundances of thirteen elements - C, O, Na, Mg, Al, Si, K, Ca,
Ti, V, Cr, Mn, and Fe - are extracted from the APOGEE spectra of these early
M-dwarfs via spectrum syntheses computed with an improved line list that takes
into account H$_{2}$O and FeH lines. This paper demonstrates that APOGEE
spectra can be analyzed to determine detailed chemical compositions of
M-dwarfs. Both exoplanet-hosting M-dwarfs display modest sub-solar
metallicities: [Fe/H]$_{Kepler-138}$ = -0.09 $\pm$ 0.09 dex and
[Fe/H]$_{Kepler-186}$ = -0.08 $\pm$ 0.10 dex. The measured metallicities
resulting from this high-resolution analysis are found to be higher by
$\sim$0.1-0.2 dex than previous estimates from lower-resolution spectra. The
C/O ratios obtained for the two planet-hosting stars are near-solar, with
values of 0.55 $\pm$ 0.10 for Kepler-138 and 0.52 $\pm$ 0.12 for Kepler-186.
Kepler-186 exhibits a marginally enhanced [Si/Fe] ratio.
