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Astron. Astrophys. 333, 231-250 (1998)

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4. Conclusions

The new model colors and bolometric corrections have been compared with the empirical relations measured from stars in the solar neighbourhood. For most colors there is good agreement; in particular, the theoretical color versus [FORMULA]   relations for U-B for B0-A0 dwarfs, V-K for A-G dwarfs, V-I for A-M dwarfs, I-K for M dwarfs, and (V-K) for G-M giants are in excellent agreement with observations as are the theoretical and observed bolometric correction relations (V-I)- [FORMULA], (I-K)- [FORMULA] for dwarfs and (V-K)- [FORMULA] for giants.

The exceptions, for the NMARCS models, are the B-V indices for K giants, M dwarfs and M giants, and the J-K indices for M dwarfs cooler than about 2800 K. The reason for these differences needs to be examined, but problems in the IR of cool dwarfs are almost certainly due to a deficient line list for H2 O (Brett 1995a). For temperatures cooler than 2500K additional opacities due to grains and polyatomic molecules presumably become important and must also be included (see e.g., Tsuji et al. 1996a, b; Allard et al. 1996). Allard et al. (1994), Allard & Hauschildt (1995), Tsuji & Ohnaka (1995), and Tsuji et al. (1995) have also modelled cool M dwarfs and brown dwarfs. See also the first successful attempt by Chabrier et al. (1996) to derive an ab initio mass-luminosity (and colors) relationship for the bottom of the main-sequence, using Brett atmospheres as boundary conditions to evolutionary models.

Missing or erroneous opacities in the blue-visual region are probably mainly responsible for the (B-V) deficiencies. Detailed comparison of spectra rather than colors would be useful in this context. The present NMARCS models use, for the iron peak elements, the same atomic line lists used by Kurucz for computing line opacities (Kurucz, 1991). We then added a few strong lines of some other species. In addition to missing atomic line opacities, there is also the possibility that some molecular opacity sources are missing in the blue-visual region. Our inclusion of the TiO a-f system had a non-negligible impact on the V band as well as the inclusion of Langhoff's (1997) electronic transition momenta dependent of internuclear distance for the [FORMULA] transition system. Newer line lists merging a larger number of transitions taken from the most updated available data bases (Kurucz, 1995b; Piskunov et al., 1995) should show further improvements in the calculated fluxes.

Cooler than 3000K most M giant stars are variable and the regular shock waves that traverse the atmospheres create a greatly extended atmosphere. The static model atmospheres discussed in this paper cannot be expected to adequately represent the cooler giants. Investigatory models of such stars have been computed by e.g. Bessell et al. (1989, 1991, 1996) and Höfner & Dorfi (1997) . Bessell et al. (1991) have computed AGB tracks for red giants and supergiants that extend as cool as 2500K. Colors and luminosities were also published for these tracks but some of these broad-band colors are not as realistic as the colors presented here because of limitations in the line opacities and methods used. The model structures, however, may not be as affected. But in a recent work, Alvarez & Plez (1997) have computed very realistic colors for mira models with the NMARCS line opacities and these offer great prospects for the more realistic spectral modelling of miras. Scholz & Takeda (1987) discuss complications in radii measurements in such extended mira models.

The ATLAS9 models fit stars hotter than 4250K very well for all the indices examined. For cooler stars, the NMARCS models with their more complete molecular opacity are preferred to ATLAS models below 4200 K for M dwarfs, and below 4000 K for M giants. Giant model colors are very similar to the NMARCS colors for temperatures hotter than 4000K.

Also the Gustafsson et al. (1975) models were inadequate for temperatures below 4500K; in fact, they yielded systematically too low abundances for stars cooler than about 4300K when model parameters were derived from the observed colors and the Ridgway et al. (1980) temperature scale (Bessell 1992). Using the NMARCS models, Bessell & Plez (1997) find no systematic trends in abundance with temperature along the giant branch in M67 and 47 Tuc. The V-K and V-I colors show little sensitivity to gravity between 6000 and 4000K. For temperatures below 3600K, lower gravity models are much redder and more extended (lower mass) models are a little redder.

On the basis of above comparisons one could expect that the model colors for different abundances, luminosities and masses should enable equally as reliable temperatures to be derived for stars of all mass and age (for very extreme cases, like very metal-poor stars more tests will be needed as different opacity sources manifest themselves). We can further expect that excellent integrated colors for clusters and galaxies can be computed by using the theoretical effective temperature-effective gravity loci from theoretical isochrones and evolutionary tracks and interpolating colors from the new model atmosphere grids.

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© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998