Measuring Fundamental Parameters of Substellar Objects. II: Masses and   Radii
  We present mass and radius derivations for a sample of very young, mid- to late M, low-mass stellar and substellar objects in Upper Sco and Taurus. In a previous paper, we determined effective temperatures and surface gravities for these targets, from an analysis of their high-resolution optical spectra and comparisons to the latest synthetic spectra. We now derive extinctions, radii, masses and luminosities by combining our previous results with observed photometry, surface fluxes from the synthetic spectra and the known cluster distances. These are the first mass and radius estimates for young, very low mass bodies that are independent of theoretical evolutionary models (though our estimates do depend on spectral modeling). We find that for most of our sample, our derived mass-radius and mass-luminosity relationships are in very good agreement with the theoretical predictions. However, our results diverge from the evolutionary model values for the coolest, lowest-mass targets: our inferred radii and luminosities are significantly larger than predicted for these objects at the likely cluster ages, causing them to appear much younger than expected. We suggest that uncertainties in the evolutionary models - e.g., in the choice of initial conditions and/or treatment of interior convection - may be responsible for this discrepancy. Finally, two of our late-M objects (USco 128 and 130) appear to have masses close to the deuterium-fusion boundary (9--14 Jupiters, within a factor of 2). This conclusion is primarily a consequence of their considerable faintness compared to other targets with similar extinction, spectral type and temperature (difference of 1 mag). Our result suggests that the faintest young late-M or cooler objects may be significantly lower in mass than the current theoretical tracks indicate. 
Subhanjoy Mohanty, Ray Jayawardhana, Gibor Basri