Near-IR spectra of red supergiants and giants -: I.: Models with solar and with mixing-induced surface abundance ratios

Context. It remains difficult to interpret the near-IR emission of young stellar populations. One main reason is our incomplete understanding of the spectra of luminous red stars. Aims. This work provides a grid of theoretical spectra of red giant and supergiant stars, that extends through optical and near-IR wavelengths. For the first time, models are also provided with modified surface abundances of C, N and O, as a step towards accounting for the changes that occur due to convective dredge-up in red supergiants or may occur at earlier evolutionary stages in the case of rotation. The aims are (i) to assess how well current models reproduce observed spectra, in particular in the near-IR; (ii) to quantify the effects of the abundance changes on the spectra; and (iii) to determine how these changes affect estimates of fundamental stellar parameters. Methods. Spectra are computed with the model atmosphere code PHOENIX and compared with a homogeneous set of observations. Although the empirical spectra have a resolution of only lambda/Delta lambda similar to 1000, we emphasize that models must be calculated at high spectral resolution in order to reproduce the shapes of line blends and molecular bands. Results. Giant star spectra of class III can be fitted extremely well at solar metallicity down to similar to 3400K, where difficulties appear in the modelling of near-IR H2O and TiO absorption bands. Luminous giants of class II can be fitted well too, with modified surface abundances preferred in a minority of cases, possibly indicating mixing in excess of standard first dredge-up. Supergiant stars show a larger variety of near-IR spectra, and good fits are currently obtained for about one third of the observations only. Modified surface abundances help reproducing strong CN bands, but do not suffice to resolve the difficulties. The effect of the abundance changes on the estimated T-eff depends on the wavelength range of observation and can amount several 100 K. Conclusions. While theoretical spectra for giant stars are becoming very satisfactory, red supergiants require further work. The model grid must be extended, in particular to larger micro-turbulent velocities. Some observed spectra may call for models with even lower gravities than explored here (and therefore probably stellar winds), and/or with more extreme abundances than predicted by standard non-rotating evolution models. Non-static atmospheres models should also be envisaged.