Heterogeneous condensation of presolar titanium carbide core-graphite mantle spherules

We investigate heterogeneous nucleation and growth of graphite on precondensed TIC grains in the gas outflows from carbon-rich asymptotic giant branch (AGB) stars employing a newly-derived heterogeneous nucleation rate taking into account of the chemical reactions at condensation. Competition between heterogeneous and homogeneous nucleations and growths of graphite is investigated to reveal the formation conditions of the TiC core-graphite mantle spherules found in the Murchison meteorite. It is shown that no homogeneous graphite grain condenses whenever TiC condenses prior to graphite in the plausible ranges of the stellar parameters. Heterogeneous condensation of graphite occurs on the surfaces of growing TiC grains, and prevents the TiC cores from reaching the sizes realized if all available Ti atoms were incorporated into TiC grains. The physical conditions at the formation sites of the TiC core-graphite mantle spherules observed in the Murchison meteorite are expressed by the relation 0.2 < nu(0.1)((M)over dot/zeta)(-1/2) L-4(1/4) < 0.7, where nu(0.1) is the gas outflow velocity at the formation site in units of 0.1 km s(-1), M-5 the mass loss rate in 10(-5) Mcircle dot year(-1), L-4 the stellar luminosity in 10(4) Lcircle dot and (M)over dot/zeta is the effective mass loss rate taking account of non-spherical symmetry of the gas outflows. The total gas pressures P-c at the formation sites for the effective mass loss rates (M)over dot/zeta = 10(-5)-10(-3) Mcircle dot year(-1) correspond to 0.01 < P-c < 0.9 dyn cm(-2), implying that the observed TiC core-graphite mantle spherules are formed not only at the superwind stage but also at the earlier stage of low mass loss rates. The constraint on the C/O abundance ratio, 1 < epsilon less than or similar to 1.03, is imposed to reproduce the observed sizes of the TiC cores. The derived upper limit of the C/O ratio is lower than the values estimated from the calculations without taking into account of heterogeneous condensation of graphite, and is close to the lower end of the C/O ratios inferred from the astronomical observations of carbon-rich AGB stars. Brief discussion is given on other types of graphite spherules.