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

1. Introduction

The mass of a star is arguably its most basic characteristic, since most stellar properties have a very steep mass dependency. Yet, it can only be directly determined for some stars in multiple systems, and for most stars it has to be inferred from more directly observable parameters, the luminosity, the chemical composition, and the evolutionary status. An accurately calibrated Mass-Luminosity (hereafter M/L) relation, or in full generality a Mass-Composition-Age/Luminosity relation, is therefore an essential astrophysical tool (e.g. Andersen 1991 , 1998). It is needed at many places to convert observable stellar light to the underlying mass, and perhaps most importantly, to derive stellar mass functions from more readily obtained luminosity functions. The latter in turn provide an essential diagnostic of star formation theories. They also represent a basic building block for galactic and stellar cluster dynamical models.

The M/L relation is fairly well constrained for solar-type and intermediate mass stars: a sizeable number of such stars in eclipsing systems have had their mass determined with better than 1% relative accuracy (Andersen 1991), and the theory of these stars approximately matches this excellent precision, when both evolutionary effects and metallicity are taken into account (Andersen 1998). For both smaller and more massive stars however, the M/L relation is significantly more uncertain, as theory and observations meet there with new difficulties.

Here we address the low-mass end of the HR diagram, below 0.6, where stellar models face two major hurdles (Chabrier & Baraffe 2000, for a recent review):

• the onset of low temperature electron degeneracy in the stellar core (Chabrier & Baraffe 1997 , 2000);

• a complex cold and high gravity stellar atmosphere, dominated by molecular and dust opacity (Allard et al. 1997; Jones & Tsuji 1997; Allard 1998).

Much progress has been made in the past few years, with the realization that an accurate atmosphere description must be used as an outer boundary condition to the stellar interior equations (Baraffe et al. 1995), and with an increased sophistication of the atmospheric models (Allard et al., in prep). State of the art models (Baraffe et al. 1998; Chabrier et al. 2000) now produce good to fair agreement with most observational colour-magnitude diagrams (Goldman et al. 1999, for an example). This lends considerable credence to their general reliability. Their description of some of the input physics however remains incomplete or approximate: some molecular opacity sources are still described by relatively crude approximations, or by line lists that remain incomplete (though vastly improved), the validity of the mixing-length approximation in the convective atmosphere is questionable, and atmospheric dust condensation and settling introduces new uncertainties at the lowest effective temperatures. The actual severity of these known shortcomings of the models is unclear, making an independent check of their M/L prediction most desirable.

Detached eclipsing M-dwarf binaries are rare, with only three known to date. Most mass determinations for Very Low Mass Stars (VLMS) are therefore instead obtained from visual and interferometric pairs, which until recently have not yielded comparable precisions. The current state of the art empirical M/L relation for M dwarfs (Henry & McCarthy 1993; Henry et al. 1999) as a result mostly rests on masses determined with 5-20% accuracy. The last two years have seen a dramatic evolution in this respect, with two groups breaking through the former 5% accuracy barrier. The first team used the 1 mas per measurement astrometric accuracy of the Fine Guidance Sensors (Benedict et al. 1999) on HST to determine system masses for three angulary resolved binaries with 2 to 10% accuracy (Franz et al. 1998; Torres et al. 1999; Benedict et al. 2000). Shortly thereafter our team demonstrated even better accuracies for masses of VLMS, of only 1-3% (Forveille et al. 1999; Delfosse et al. 1999b), by combining very accurate radial velocities with precise angular separations from adaptive optics. In a companion paper (Ségransan et al. 2000) we determine a dozen new or improved masses, with the same method and with accuracies that now range between 0.5 and 5%. The same paper also presents improved masses for two of the three known eclipsing M-dwarf systems, with 0.2% accuracy. Here we take advantage of this wealth of accurate new data, and reassess the VLMS M/L relation on a much firmer ground.

In Sect. 2 we briefly describe the sample of accurately determined very low stellar masses. We then discuss the resulting empirical M/L relation in Sect. 3, and compare it with theoretical models in Sect. 4.

© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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