The Lambert Problem

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David Lambert was one of the first to show convincingly that the observationally inferred and theoretically predicted abundances for CNO nuclei did not agree. He and his collaborators made extensive efforts to provide reliable abundances for stars, and especially for the isotopic abundances of C, N and O, which directly reflect thermonuclear processing. Iben(1964) showed that dredge-up by the outer convection zone would bring to the surface isotopes of CNO which had been processed. It gradually became clear that more material from nuclearly processing regions was required; and "additional mixing" was needed to match the observations. This observational puzzle is deeply connected to an inadequacy in the theoretical treatment of the fluid motion of stellar plasma. The effects of internal gravity waves, which are clearly visible in numerical simulations, are generally neglected in stellar evolutionary calculations. The correction of this error has deep implication for the evolution of stars, galaxies, and the chemical elements; the effect increases with stellar mass. Finally we note that these gravity waves may provide a resolution to the "convective zone problem" of Bahcall, et al. (2004), another conundrum in which Lambert is involved.

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