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

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5. Conclusions

Empirical masses of 0.2 to 10% accuracy validate the near-IR Mass/Luminosity relations predicted by the recent stellar models of Baraffe et al. (1998) and Siess et al. (2000), down to [FORMULA]0.1 [FORMULA]. They also point out some low level ([FORMULA]0.5 mag) deficiencies of these models in the V band. Perhaps more importantly however, the V band M/L diagram represents direct evidence for an intrinsic dispersion around the mean M/L relation. This had previously remained hidden in the measurement noise, but there is, as theoreticians have kept telling us, no such thing as one single M/L relation for all M dwarfs. This is particularly true for the visible bands, while the dispersion in the near-IR JHK bands is much lower. Comparisons between measured masses and theoretical models will therefore increasingly depend on metallicity measurements for individual systems, which are not easily obtained.

The [FORMULA]0.5 magnitude discrepancy between observational and model masses derived from visible photometry has some consequences for mass functions determination. As mass cannot be determined for volume-limited samples, the mass function is always obtained from a luminosity function, by writing that

[EQUATION]

and the slope of the M/L relation therefore plays a central role in its derivation. Below 0.5[FORMULA] the d[FORMULA]dM slope of the empirical M/L relation is steeper than that of the BCAH models and shallower than for the SDF ones, by 10 to 20%. Their use will therefore respectively underestimate and overestimate the number of lower mass stars by this amount. Probably more seriously, the large dispersion around the V band M/L relation will introduce large Malmquist-like biases in the derived mass function, which would need an excellent characterization of this dispersion to be corrected. The infrared relations have both better agreement with the observations and much lower dispersion. We strongly recommend that they be used rather than the V band relations, whenever possible.

Note added in proof: After the paper was accepted, Pavel Kroupa pointed out that we have omitted the Kroupa, Tout & Gilmore (1993, MNRAS 262, 545) relation in our comparison of the new data with published empirical mass-luminosity relations. The Kroupa et al. relation is in excellent agreement with the new data, except may be for the very end of main sequence ([FORMULA]). We plan to show in a future paper the comparison with this empirical relation, which provides a significantly better description of the new data than the more commonly used Henry & McCarthy (1993) piece-wise linear relations and does not suffer from discontinuous derivatives. We are grateful to Pavel Kroupa for this comment.

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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