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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 youngstellar populations. One main reason is our incomplete understanding ofthe spectra of luminous red stars. Aims: This work provides a grid oftheoretical spectra of red giant and supergiant stars, that extendsthrough optical and near-IR wavelengths. For the first time, models arealso provided with modified surface abundances of C, N and O, as a steptowards accounting for the changes that occur due to convectivedredge-up in red supergiants or may occur at earlier evolutionary stagesin the case of rotation. The aims are (i) to assess how well currentmodels reproduce observed spectra, in particular in the near-IR; (ii) toquantify the effects of the abundance changes on the spectra; and (iii)to determine how these changes affect estimates of fundamental stellarparameters. Methods: Spectra are computed with the model atmospherecode PHOENIX and compared with a homogeneous set of observations.Although the empirical spectra have a resolution of onlyλ/Δλ ˜ 1000, we emphasize that models must becalculated at high spectral resolution in order to reproduce the shapesof line blends and molecular bands. Results: Giant star spectra ofclass III can be fitted extremely well at solar metallicity down to~3400 K, where difficulties appear in the modelling of near-IR H2O andTiO absorption bands. Luminous giants of class II can be fitted welltoo, 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 fitsare currently obtained for about one third of the observations only.Modified surface abundances help reproducing strong CN bands, but do notsuffice to resolve the difficulties. The effect of the abundance changeson the estimated Teff depends on the wavelength range ofobservation and can amount several 100 K. Conclusions: Whiletheoretical spectra for giant stars are becoming very satisfactory, redsupergiants require further work. The model grid must be extended, inparticular to larger micro-turbulent velocities. Some observed spectramay call for models with even lower gravities than explored here (andtherefore probably stellar winds), and/or with more extreme abundancesthan predicted by standard non-rotating evolution models. Non-staticatmospheres models should also be envisaged.Selected theoretical spectra (see text) can be retrieved in FITS formatat CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/468/205
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