3. Metallicity dependence of SK for M-dwarfs
In addition to gravity, metallicity affects the surface brightness at a given colour. Given the steepness of the () relation, however, the dependence of the observational data on metallicity is easily obliterated by errors in . It is more readily detectable in the infrared K-band because is a much shallower function of colour.
The models suggest that the metallicity dependence appears only at temperatures sufficiently low that molecules are present. For giants and supergiants with K, corresponding to , the models of Alibert et al. (1999) indicate a very small dependence on metallicity. At these higher temperatures, and at given or vary by less than 0.05 mag for metallicities between [M/H] = 0 and -0.7. For dwarfs, the main metallicity effects appear for (BCAH98), a regime which is largely unexplored for giants.
In Fig. 2ab, we compare the observed values of vs. and for the 16 dwarfs of L96 supplemented by YY Gem and the Sun with the predictions of the models of BCAH98 for main-sequence dwarfs. The theoretical curves refer to ZAMS models with solar metallicity [M/H] (solid curves) and to models for stars aged 10 Gyr with metallicities -0.5 (long dashes) and -1.5 (short dashes). Pre-main-sequence stars of solar composition aged years (dotted curves) and ZAMS stars of the same colour agree closely in surface brightness, except for very late spectral types where the -yrs isochrone is sufficiently far from the ZAMS for gravity effects to become apparent. For these pre-main-sequence stars is enhanced and differs from ZAMS dwarfs in the same way as is evident for late-type giants in Fig. 1.
Fig. 2a demonstrates that the main-sequence models reproduce the observed level of , its variation with , and the spread with metallicity exceedingly well. The agreement between observation and theory is less good for vs. in Fig. 2b because, as noted above, the theoretical colours of solar-metallicity M-stars with which involve V are too blue (by about half a magnitude). This uncertainty in V is much smaller for dwarfs of lower metallicity. For the purpose of determining radii via Eq. (2), we provide the surface brightness values of the BCAH98 models in Table 1, except for of stars with solar metallicity for which we approximate the data for the eight L96 YD dwarfs, YY Gem, and the Sun by the linear relation
The limited statistics of the L96 sample does not warrant a higher-order fit, but the real relation for solar-metallicity stars will certainly show some structure caused by molecule formation and the onset of convection in the optically thin layers of the atmosphere, as does the () relation at .
Table 1. Model values of the surface brightness in the K-band as functions of and for ZAMS stars with solar metallicity and stars aged 10 Gyr with 1/3 solar metallicity (from BCAH98). The K-band magnitudes are on the CIT system.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999