Mass-Luminosity Relationship and Lithium Depletion for Very Low Mass Stars

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Abstract
We derive mass-luminosity relationships for very low mass stars (0.06 < m/M☉ < 0.6) for different metallicities. Calculations are conducted with the different nongray atmosphere models presently available to illustrate the uncertainties in the stellar models. The theoretical mass-magnitude relation reproduces accurately the observed relationship in the V band (Henry & McCarthy) but still underestimates the flux in the K band by ~0.5 mag, a consequence of the still inaccurate water opacities. Calculations based on the gray approximation are shown to yield incorrect results over the entire mass range of interest. We also show that the fate of objects near the hydrogen-burning limit depends significantly on the treatment of the atmosphere. Nongray effects yield cooler and less luminous objects for a given mass near the stellar/substellar transition, and thus a lower hydrogen-burning minimum mass, m ≈ 0.07 M☉, for solar metallicity. The depletion of lithium along evolution is considered in detail, and we give age versus lithium-abundance relations that provide useful guides to determine the mass and the age of spectroscopically observed low-mass objects.