Elemental abundances of M dwarfs based on high-resolution near-infrared spectra: Verification by binary systems

M dwarfs are prominent targets of planet search projects, and their chemical composition is crucial to understanding the formation process or interior of orbiting exoplanets. However, measurements of elemental abundances of M dwarfs have been limited due to difficulties in the analysis of their optical spectra. We conducted a detailed chemical analysis of five M dwarfs (T_eff ∼ 3200-3800 K), which form binary systems with G/K-type stars, by performing a line-by-line analysis based on high-resolution (R ∼ 80000) near-infrared (960-1710 nm) spectra obtained with CARMENES (Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Échelle Spectrographs). We determined the chemical abundances of eight elements (Na, Mg, K, Ca, Ti, Cr, Mn, and Fe), which are in agreement with those of the primary stars within measurement errors (∼0.2 dex). Through the analysis process, we investigated the unique behavior of atomic lines in a cool atmosphere. Most atomic lines are sensitive to changes in the abundance of not only the corresponding elements but also other elements, especially dominant electron donors such as Na and Ca. The Ti I lines show a negative correlation with the overall metallicity at T_eff < 3400 K due to the consumption of neutral titanium by the formation of TiO molecules. These findings indicate that to estimate the overall metallicity or the abundance of any element correctly, we need to determine the abundances of other individual elements consistently.