Measuring fundamental parameters of substellar objects. I. Surface gravities

We present an analysis of high-resolution optical spectra for a sample of very young, mid- to late-M, low-mass stellar and substellar objects: 11 in the Upper Scorpius association, and two (GG Tau Ba and Bb) in the Taurus star-forming region. Effective temperatures and surface gravities are derived from a multiple-feature spectral analysis using TiO, Na I, and K I, through comparison with the latest synthetic spectra. We show that these spectral diagnostics complement each other, removing degeneracies with temperature and gravity in the behavior of each. In combination, they allow us to determine temperature to within 50 K and gravity to within 0.25 dex, in very cool young objects. Our high-resolution spectral analysis does not require extinction estimates. Moreover, it yields temperatures and gravities independent of theoretical evolutionary models ( although our estimates do depend on the synthetic spectral modeling). We find that our gravities for most of the sample agree remarkably well with the isochrone predictions for the likely cluster ages. However, discrepancies appear in our coolest targets: these appear to have significantly lower gravity ( by up to 0.75 dex) than our hotter objects, even though our entire sample covers a relatively narrow range in effective temperature ( similar to 300 K). This drop in gravity is also implied by intercomparisons of the data alone, without recourse to synthetic spectra. We consider, and argue against, dust opacity, cool stellar spots, or metallicity differences leading to the observed spectral effects; a real decline in gravity is strongly indicated. Such gravity variations are contrary to the predictions of the evolutionary tracks, causing improbably low ages to be inferred from the tracks for our coolest targets. Through a simple consideration of contraction timescales, we quantify the age errors introduced into the tracks through the particular choice of initial conditions and demonstrate that they can be significant for low-mass objects that are only a few megayears old. However, we also find that these errors appear insufficient to explain the magnitude of the age offsets in our lowest gravity targets. We venture that this apparent age offset may arise from evolutionary model uncertainties related to accretion, deuterium burning and/or convection effects. Finally, when combined with photometry and distance information, our technique for deriving surface gravities and effective temperatures provides a way of obtaining masses and radii for substellar objects independent of evolutionary models; radius and mass determinations are presented in Paper II.