D_CO(left) and C₂(right panel) indices versus (J − K) colour for stars in the Milky Way and the LMC. The oxygen- and carbon-rich LMC stars (filled black and red dots, respectively) are from our own SINFONI observations, the K (green open squares), M (black diamonds), C (red asterisks), and S (red asterisks with square around) stars are taken from the SpeX library of Rayner et al. (2009). The C-rich spectra in the Milky Way (orange crosses) are taken from the library of Lançon & Mouhcine (2002). Typical error bars are shown in the upper right corner of the left panel. In the left panel, the solid line denotes the relation for LMC carbon-rich stars from Lyubenova et al. (2010, Eq. (3)), the dashed line (Eq. (5) in the same paper) represents the relation for the Milky Way spectra of Lançon & Mouhcine (2002).