Astron. Astrophys. 351, 619-626 (1999)

5. Discussion and conclusions

The accurate masses and absolute magnitudes that we have obtained for the Gl 570BC system represent a new benchmark for model calculations (e.g. Baraffe et al. 1998) and an independent check of the empirical mass-luminosity relations (HMcC). The constraints which they bring to the models are largely complementary to those coming from the eclipsing binaries, whose absolute radii can be determined very accurately but whose larger distances on the other hand contribute significant uncertainties to the absolute magnitudes.

As long emphasized by theoreticians, and by observers of more massive stars (e.g. Andersen 1991), there is however no such thing as one single mass-luminosity relation: stellar luminosities depend on chemical composition as well as on mass (in general they depend on age too, though not in the age and mass range discussed here). Quantitative metallicity determinations however are notoriously difficult for M dwarfs (e.g. Viti et al. 1997; Valenti et al. 1998). Observers in this field usually have to resort to photometric metallicity estimators (Leggett 1992) which are only approximately calibrated, or otherwise assume by default a solar metallicity. Thanks to its physical association with the hotter Gl 570A (K4V), the Gl 570BC pair represents a rare case of two M dwarfs with a very well determined spectroscopic metallicity. Its accurate masses are thus fortunately matched with excellent metallicities. Hearnshaw (1976) first measured the metallicity of Gl 570A from high resolution electronographic spectra and obtained [Fe/H]=+0.010.15. More recently, Feltzing & Gustafsson (1998) measured [Fe/H]=0.040.02(random)0.1(systematic) from high S/N R=10⁵ echelle CCD spectra. These authors find some evidence for NLTE overionisation of Fe into Fe⁺, but the derived elemental Fe abundance is unaffected, as Fe is overwhelmingly neutral in the photosphere of a K4 dwarf. Quite conveniently for comparison with published models, the Gl 570 system thus has a truly solar metallicity.

Fig. 3 compares the mass and luminosity of the two components of Gl 570BC with the Baraffe et al. (1998) 10 Gyr solar-metallicity isochrone. These models consistently combine stellar evolution models (e.g. Chabrier & Baraffe 1997) and non-grey atmospheric models (Allard & Hauschild 1995; Hauschild et al. 1999). The present generation of these evolutionary models still uses non-dusty atmospheres, but dust only becomes relevant at effective temperatures significantly lower than those of Gl 570BC (Allard 1998). The Baraffe et al. models are consistently slightly brighter in all 3 bands than the two stars, by 0.08 to 0.15 magnitude. While this level of agreement is already very comforting, the discrepancies are significant at the 3 levels and may point towards remaining low level deficiencies of the theoretical models. If one adopts the measured J and H band flux ratios, rather than the smaller values that we have estimated from the K band measurement, the agreement with the models improves only slightly for the primary star, as its magnitude only weakly depends on the exact value of the large flux ratio. At the same time this choice degrades the agreement for the fainter star by a larger factor, and the overall agreement with the models is significantly worse.

Fig. 3. Near-IR Mass-Luminosity diagrams for mid-M dwarfs. The square symbols with thick error bars correspond to the two components of Gl 570BC, and the thin error-bars represent data from HMcC. The solid and dot-dashed lines respectively represent the empirical HMcC analytical Mass-Luminosity relation and the theoretical [M/H]=0.0 10 Gyr isochrone of Baraffe et al. (1998).

Fig. 3 also shows the data points of HMcC, as well as their analytic representation of those data. The agreement is essentially perfect with the J band HMcC relation, while the H and K band relations are slightly discrepant, by respectively 0.1 and 0.15 magnitudes. We note that the HMcC mass-luminosity relations are only consistent with the empirical M dwarf colours of Leggett (1992) at this 0.10-0.15 magnitude level, even though the HMcC photometry mostly traces back to Leggett (1992). This is because the HMcC mass-magnitude relations for J, H and K were adjusted independently, without explicit forcing of colour consistency. The perfect agreement with the J band HMcC fit is therefore probably fortuitous to some extent, and the 0.10 to 0.15 discrepancy for the H and K bands probably represents a more realistic estimate of the accuracy of those analytic fits around 0.5 .

© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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