Constraints on grain formation around carbon stars from laboratory studies of presolar graphite

Abstract

We report the results of an investigation into the physical conditions in the mass outflows of asymptotic giant branch (AGB) carbon stars that are required for the formation of micron-sized presolar graphite grains, with and without previously formed internal crystals of titanium carbide (TiC). A lower mass limit of 1.1 M⊙ for stars capable of contributing grains to the solar nebula is derived. This mass limit, in conjunction with a mass-luminosity relation for carbon stars, identifies the region of the H-R diagram relevant to the production of presolar graphite. Detailed dynamical models of AGB outflows, along with constraints provided by kinetics and equilibrium thermodynamics, indicate that grain formation occurs at radii from 2.3 to 3.7 AU for AGB carbon stars in the 1.1-5 M⊙ range. This analysis also yields time intervals available for graphite growth that are on the order of a few years. By considering the luminosity variations of carbon stars, we show that grains formed during minima in the luminosity are likely to be evaporated subsequently, while those formed at luminosity maxima will survive. We calculate strict upper limits on grain sizes for graphite and TiC in spherically symmetric AGB outflows. Graphite grains can reach diameters in the observed micron size range (1-2 µm) only under ideal growth conditions (perfect sticking efficiency, no evaporation, no depletion of gas species contributing to grain growth), and then only in outflows from carbon stars with masses ≲ 2.5 M⊙. The same is true for TiC grains that are found within presolar graphite, which have mean diameters of 24 ± 14 nm. In general, the mass-loss rates that would be required to produce the observed grain sizes in spherically symmetric outflows are at least an order of magnitude larger than the maximum observed AGB carbon star mass-loss rates. These results, as well as pressure constraints derived from equilibrium thermodynamics, force us to conclude that presolar graphite and TiC must form in regions of enhanced density (clumps, jets) in AGB outflows having small angular scales. As shown in the companion paper by Croat et al., the enrichment of ¹²C in many AGB graphites, and the overabundances of the s-process elements Mo, Zr, and Ru in the carbides found within them, often greatly exceed the values observed astronomically in AGB outflows. These observations not only lend further support to the idea that the outflows are clumpy, but also imply that the outflowing matter is not well mixed in the circumstellar envelope out to the radii where grain condensation takes place.