The Depth of the Convective Envelope on the Lower Main Sequence and the Depletion of Lithium.

Herbig's observations strongly indicate that extensive lithium depletion must occur after stars of about solar type reach the main sequence. Solar models constructed using opacity tables which include boundbound effects have envelopes which reach down to about T = 2 X 100. Nevertheless, these models are not deep enough, by a small, but we believe significant, amount, to deplete Li7. Similar conclusions follow from a study of homogeneous models from 1.2 Mo to 0.55 M0. A suggestion that extensive mass loss could be responsible for the Li depletion is examined but is found to require a rate of mass loss about 3 orders of magnitude higher than is now believed to occur for the Sun. "Convective-overshoot" effects are roughly estimated, and we conclude that penetration to depths of about 3 X 106 K is energetically possible only for convective elements starting at the very top of the convective envelope where log P < 7. We estimate the probability that such elements actually do reach to depths of T = 3 X 100 by mixing length analogously to the mean free path in kinetic theory. Taking the mean free path at every point comparable to the size of the element at every point, and taking the initial element size to be comparable to the initial local pressure scale height, we find the probability of penetration to be completely negligible, and on this basis would conclude that convective overshooting does not enhance the lithium-depletion rate. However, a firm physical justification for a calculation of this type does not exist. We feel therefore that a theory of convective overshoot must be developed along the lines initiated by -but with careful treatment of the topmost layers-before the question of enhanced lithium depletion by convective overshoot can be finally settled.