4. Comparison to theoretical models
Fig. 3 compares the empirical M/L data with the corresponding 5 Gyr theoretical isochrones (for which even the lowest-mass stars on the plot have settled on the main sequence) of Baraffe et al. (1998; hereafter BCAH) and Siess et al. (2000; hereafter SDF). For very low mass stars these two sets of models are up to now the only ones to use realistic model atmospheres as outer boundary conditions to the stellar interior equations. This has been found necessary for accurate results in this mass range (Chabrier et al. 1996). BCAH use atmospheres from Hauschildt et al. (1999), while SDF use the older Plez (1992) models. Besides this, and the different input physics that they use, the two sets of models differ by the technique used to compute observational quantities. SDF use the empirical bolometric correction tables of Kenyon & Hartmann (1995) to deduce absolute magnitudes in the various photometric bands from their theoretical bolometric luminosities and effective temperatures. BCAH on the other hand adopt a purely ab initio approach, and compute the absolute magnitudes from the stellar radii, the model atmosphere spectra, and the transmission profile of the photometric filters.
At the scale of Fig. 3 the BCAH and SDF models are nearly indistinguishable for the infrared bands, and both produce an impressive agreement there with the observational data. This is particulary striking for the K band, where many measurements define the M/L relation. The same is apparently true for J and H, where more data would nonetheless be welcome to confirm this behaviour.
In the V band (Fig. 3) on the other hand, neither of the two sets of models reproduces the observations perfectly. The BCAH models and the observations agree well above 0.5 , though with significant dispersion, but they diverge somewhat for lower masses. Below 0.2 , the solar metallicity models are systematically too luminous by 0.5 magnitude. As most of the bolometric flux of such stars emerges in the near-IR bands, where the agreement is excellent, the models necessarily provide a good account of the relation between mass and bolometric magnitude. Their overall description of the stars is therefore most likely correct, and the V band discrepancy probably points to a relatively localized problem in the models. The two leading explanations for this discrepancy (Baraffe & Chabrier, private communication) are either a V band opacity source that would be missing in the atmospheric models, or some low level problem in the physical description of the shallower atmospheric levels which emit the visible flux.
The SDF models by contrast are 0.5 mag too luminous in the V band above 0.3, produce an excellent agreement with the observations for 0.2, and look sub-luminous for 0.1. Here again, the excellent near-IR agreement with the observations indicates that these models nicely reproduce the relation between mass and bolometric magnitude, and the discrepancy rests in the V band bolometric correction. Indeed, the SDF models mostly target PMS stars and the Kenyon & Hartmann (1995) bolometric correction that they use applies for T Tauri stars, which have lower gravity than main sequence stars and hence somewhat different colours. The use of observational bolometric correction, which by definition are unaffected by missing opacity sources, on the other hand most likely explains why the SDF models agree better with the V band observations at 0.2.
The characteristics of very low mass stars are frequently derived from photometry in the redder CCD bands, R and especially I, where these objects are brighter than in the V band. The validity of the theoretical M/L relation for these red bands is thus of significant interest, but too few VLMSs with accurate masses have known luminosities in the R, I, or z filters to provide a fully empirical verification. One can note however that Baraffe et al. (1998) observe that below 3700 K the BCAH model and colours are too blue by 0.5 mag at a given luminosity, while colours which don't involve the V band are much better predicted. Since the BCAH model are also 0.5 mag too luminous for their mass, this suggests that the atmospheric models have a problem that is specific to the V band. The model M/L relations for the R, I and z bands are then probably more nearly correct. If valid this inference would suggest that the root of the problem rests in the V band opacity rather than in the physical description of the visible photosphere, which would probably affect a broader wavelength range.
© European Southern Observatory (ESO) 2000
Online publication: December 15, 2000