Lithium depletion in fully convective pre-main-sequence stars

We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully convective, pre-main-sequence stars of mass M less than or similar to 0.5 M.. Previous numerical work relies on still uncertain physics (atmospheric opacities and convection, in particular) to calculate the effective temperature as a unique function of stellar mass. We assume that the star's effective temperature, T-eff, is fixed during Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on T-eff, M, and composition. Our calculations yield the radius, age, and luminosity of a pre main-sequence star as a function of lithium depletion. This allows for more direct comparisons with observations of lithium-depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with Basri, Marcy, & Graham, we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating Galactic clusters younger than 100 Myr (i.e., those with contracting stars of M greater than or similar to 0.08 M.) and for constraining the masses of lithium-depleted stars.