Accurate masses of very low mass stars: IV Improved mass-luminosity relations

We present improved visual and near-infrared empirical mass-luminosity relations for very low mass stars (M$<$0.6~\Msol). These relations make use of all stellar masses in this range known with better than 10% accuracy, most of which are new determinations with 0.2 to 5% accuracy from our own programme, presented in a companion paper. As predicted by stellar structure models, the metallicity dispersion of the field populations induces a large scatter around the mean V band relation, while the infrared relations are much tighter. The agreement of the observed infrared mass-luminosity relations with the theoretical relations of Baraffe et al. (1998) and Siess et al. (2000) is impressive, while we find an increasingly significant discrepancy in the V band for decreasing masses. The theoretical mass-luminosity relation which is insufficiently steep, and has introduced some errors in the local stellar mass functions derived from V band luminosity functions.