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Astron. Astrophys. 364, 217-224 (2000)

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3. Visible and infrared mass/Luminosity relations

The masses are listed in Table 3, with the individual absolute magnitudes derived from Table 1 and Table 2 for the four photometric bands (V, J, H and K) which have significant numbers of measurements. Fig. 1 shows the M/L relations for these 4 photometric bands. As can be seen immediately in Fig. 1, [FORMULA]20 stars define the V and K relations, while the J and H ones still have smaller numbers of stars. A number of systems still lack magnitude difference measurements in those two bands.

[FIGURE] Fig. 1. V, J, H and K band M/L relations. The circles are data from Henry & McCarthy (1993), Torres et al. (1999), Henry et al. (1999), Benedict et al. (2000) and Metcalfe et al. (1996). The triangles represent our recent mesurements (Ségransan et al. 2000, in prep.; and Forveille et al. 1999). The masses and luminosities used in this figure are also listed in Table 3. The two curves represent the piecewise linear relation of Henry & McCarthy (1993; dotted line) and our polynomial fit (solid line).


[TABLE]

Table 3. Masses and absolute magnitudes for the M dwarfs used in the M/L relation. The mass references are Met96 for Metcalfe et al. (1996), Hen99 for Henry et al. (1999), Hen93 for Henry & McCarthy (1993), Mar98 for Martin et al. (1998), Tor99 for Torres et al. (1999), Ben00 for Benedict et al. (2000), Seg00a for Ségransan et al. (2000), Seg00b for Ségransan et al. (in prep.) and For99 for Forveille et al. (1999). When relevant we have modified the masses from Henry & McCarthy (1993) and Henry et al. (1999) to reflect a more accurate parallax in Table 1 than was available to these authors. The individual absolute magnitudes are determined from the system magnitudes and parallaxes listed in Table 1, with the magnitude differences of Table 2.


Fig. 2 presents the relation between stellar mass and the V-K colour index. This relation probably has too large an intrinsic dispersions to be generally useful, and is provided here mostly for illustration, and as a warning to potential users of similar relations.

[FIGURE] Fig. 2. mass-colour (V-K) relation for M dwarfs. The three curves are 5 Gyr theoretical isochrones from Baraffe et al. (1998) for two metallicities and our polynomial fit. The Siess et al. (2000) model are represented for 5 Gyr and solar metallicity with asterisks.

Fig. 1 shows the piecewise-linear relations adjusted by Henry & McCarthy (1993) to the J, H and K band data then available to them, and their piecewise-quadratic relation for the V band, with its Henry et al. (1999; V band) update for the lower masses. These relations provide a reasonable description of the new data, but they do show significant discrepancies, in particular around their breakpoints. Clearly the quality of the new masses warrants the use of higher order polynomials. We have found that the following fourth degree polynomials provide good descriptions of the data in Fig. 1 and Fig. 2:

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

One striking characteristic of Fig. 1 is the very different scatters in its V and K diagrams. The V plot displays considerable dispersion around a mean relation, and some of its best measurements are also some of the most discrepant. The K plot on the other hand shows a one to one relation between Mass and Luminosity, and its (mild) outliers are systems with larger than average errorbars. The J and H plots also have little dispersion, to the extent that this can be assessed from their smaller number of measurements. The V band scatter is much larger than the measurement errors, which on average are actually somewhat smaller for V than for K. This different behaviour of the visual and infrared bands, first seen so clearly here, is predicted by all theoretical models, as discussed for instance in the recent review by Chabrier & Baraffe (2000). It results from the metallicity dispersion of the solar neighbourhood populations, through the interplay of two physical mechanisms:

  • a larger metallicity increases the atmospheric opacity in the visible range, which is dominated by TiO and VO molecular bands. For a given bolometric luminosity it therefore shifts the flux distribution towards the infrared;

  • a larger metallicity decreases the bolometric luminosity for a given mass.

In the visible bands both effects work together, to decrease the visible luminosity of the more metal-rich stars at a given mass. In the near-infrared on the other hand, the redward shift of the flux distribution of the metal-rich stars counteracts their lower bolometric luminosity. The models therefore predict that infrared absolute magnitudes are largely insensitive to metallicity, and our empirical M/L relations confirm this.

At visible wavelengths on the other hand, metallicity determinations now become a crucial limiting factor in accurate comparisons with stellar models, as has long been the case for more massive stars (e.g. Andersen 1991). Quantitative metallicity measurements of M dwarfs are unfortunately difficult in the optical range (e.g. Valenti et al. 1998), but near-IR spectroscopy offers better prospects (Allard, private communication). GJ 2069A and Gl 791.2 represent spectacular illustrations of the intrinsic dispersion of the V band M/L relation, as already discussed in their respective discovery paper (Delfosse et al. 1999a; Benedict et al. 2000): these four stars are underluminous by [FORMULA]2 magnitudes for their masses, compared to solar metallicity models and to other stars. We recently discovered an additional faint component (Beuzit et al., in prep.) in GJ 2069A, which, if anything, further slightly increases its distance from a solar metallicity M/L. This discrepancy is best explained if the Gl 791.2 and GJ2069 systems are metal-rich by [FORMULA]0.5 dex. Their near-IR absolute magnitudes should be much more consistent with the average relations, but have not yet been measured.

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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