features, thereby enhancing the equivalent width (McWilliams & Lambert 1984). Another possible contributor is the differing depth of the line formation region in the dwarfs versus the giants, which is fixed by the H$^{-}$ opacity. As described by Gray (1992) higher surface gravity results in a higher electron pressure (and thus H$^-$ column density). This brings the CO line formation region closer to the stellar surface reducing $N_{CO}$ according to the following proportionality: $$P_e \sim g^{1/3} \sim N_{H^-} \sim 1/N_{CO}$$ In any case, this luminosity dependence of the band strength gives an excellent empirical discriminant between giants and dwarfs, which we exploit below to develop a two dimensional spectral index.

To discern surface gravity effects between the super–giants and giants or between sub–giants and dwarf stars requires more careful study. A detailed examination of line strengths as a function of surface gravity at a fixed temperature reveal the expected trends. However, this behavior does not reveal itself in the coarse analysis afforded by our narrow–band indices.

While the temperature and luminosity sensitivities outlined above can provide good spectral classification in many instances, discriminants which do not rely on absolute line strength are required when a star is subject to near-infrared 