## 5. Radii of main-sequence M-dwarfsIn this section, we test our results on the 12 YD/OD stars of L96 which serve as calibrators and then apply them to a sample of 60 single or presumed single YD/OD main-sequence stars. The colour-magnitude diagram of these stars is shown in Fig. 3b. Six K-stars are from Reid & Gizis (1997) (stars) and 53 M-stars from Henry & McCarthy (1993) (small solid and open circles). The L-star GD165B represents the transition to the brown-dwarf regime (asterisk). We consider the calibrator stars first. In Table 2, we compare the L96 radii with those obtained from the Barnes-Evans type relations and () and from : -
Column 9: Radii of YD or [M/H] stars derived from the observed with Eqs. (2) and (6). Radii of OD stars obtained correspondingly, but with the theoretical relation for [M/H] of Table 1 instead of Eq. (6). -
Column 10: Radii obtained from the observed with the theoretical () relations of Table 1 for the [M/H] = 0 or the [M/H] = -0.5 stars. -
Column 11: Radii derived from with Eq. (7) without regard of metallicity, assuming the stars to be on the ZAMS.
The radii in Column 11 and the YD radii in Column 9 agree with the L96 radii within 5% or log which reflects the goodness of the fits. The small differences between the radii in Columns 10 and 8, on the other hand, demonstrate the close agreement between theory and observation.
Application of the Barnes-Evans type relations to the complete
sample of 60 K/M dwarfs requires at least a rough estimate of their
metallicity. For this purpose, we divide the sample into a
Column 12 of Table 2 and Column 11 of Table 3 list the radii given by Lacy (1977) adjusted to the parallaxes used here. Compared with Lacy's results, our radii are smaller by up to %. Fig. 4 shows that there is a systematic trend for the difference between Lacy's radii and those determined by L96 or, for the addtional stars, from our Barnes-Evans type relations . Very similar pictures obtain for the radii derived from the Barnes-Evans type relation () (Table 3, Column 9) or directly from (Table 3, Column 10, both not shown). The deviation of Lacy's from our radii assumes a maximum at spectral type K7 and vanishes for early K and for late M dwarfs. Much of this is due to the different surface brightness calibrations for giants (used by Lacy) and dwarfs (used here) which reach a maximum separation at , , or spectral class K7 (Fig. 1). The remainder is due to differences in the individual giant relations used by Lacy (Barnes & Evans 1976) and by us (Eq. [3] and Dumm & Schild 1997). Lacy discussed a deviation of similar magnitude and colour-dependence between the surface brightness of giants and the theoretical ZAMS dwarf models of Copeland et al. (1970). He interpreted it as being entirely due to inadequacies of the models. We now know that (i) the surface brightness of mid-K to mid-M dwarfs is, in fact, higher than that of giants of the same colour and (ii) the recent dwarf models (BCAH98) predict somewhat larger radii than the early models which reduces the discrepancy noted by Lacy (1977).
Finally, we discuss the systematic errors in our radius calibration
which is tied to the observational results of L96 and to the
theoretical predictions of BCAH98. Our radius scale for stars of
near-solar metallicity is based on the results of L96 which may still
be in error by some % or 0.03 in
log © European Southern Observatory (ESO) 1999 Online publication: July 26, 1999 |