Although mainstream SiC grains, the major group of presolar SiC grains found in meteorites, are believed to have originated in the expanding envelope of asymptotic giant branch (AGB) stars during their late carbon-rich phases, their Si isotopic ratios show a distribution that cannot be explained by nucleosynthesis in this kind of star. Previously, this distribution has been interpreted to be the result of contributions from many AGE stars of different ages whose initial Si isotopic ratios vary owing to the Galactic chemical evolution of the Si isotopes. This paper presents a new interpretation based on local heterogeneities of the Si isotopes in the interstellar medium at the time the parent stars of the mainstream grains were born. Recently, several authors have presented inhomogeneous chemical evolution models of the Galactic disk in order to account for the well-known evidence that F and G dwarfs of similar age show an intrinsic scatter in their elemental abundances. First we report new calculations of the s-process nucleosynthesis of the Si and Ti isotopes in four AGE models (1.5, 3, and 5 M-. with Z = 0.02; 3 M-. with Z = 0.006). These calculations are based on the release of neutrons in the He intershell by the C-13 source during the interpulse periods followed by a second small burst of neutrons released in the convective thermal pulse by the marginal activation of the Ne-22 source. In the 1.5 and 3 M-. models with solar metallicity the predicted shifts of the Si isotopic ratios in the stars' envelope are much smaller (<30 parts per thousand, for the Si-29/Si-28 ratio and <40 parts per thousand, for the Si-30/Si-28 ratio; the two ratios are normalized to solar) than the range observed in the mainstream grains (up to 180 parts per thousand). Isotopic shifts are of the same order as in the SiC grains for the 5 M-. and Z = 0.006 models, but the slope of the Si-29/Si-28 versus Si-30/Si-28 correlation line is much smaller than that of the grains. We also show that none of the models can reproduce the correlations between the Ti and Si isotopic ratios measured in the mainstream grains as the result of s-process nucleosynthesis only. To explain the distribution of the grains' Si isotopic compositions, we constructed a simple Monte Carlo model in which contributions from classic Type Ia, Type Ia sub-Chandrasekhar, and Type II supernova (SN) models of different masses were admixed in a statistical way to material with a given Si isotopic composition. For four different starting compositions (average composition of the mainstream grains corrected for AGE contributions, solar composition, 100 parts per thousand and 200 parts per thousand deficits in Si-29 and Si-30 relative to solar) we show that, with the appropriate choice of; two parameters, the distribution of the Si isotopic ratios in the mainstream grains can be successfully reproduced. The parameters to be adjusted ape the total number of SN sources selected and the fraction of the material ejected from each SN that is mixed to the starting material. An upward adjustment of the supernova yield of Si-29 relative to the other Si isotopes by a factor 1.5 was also introduced. Using current SN yields and Galactic chemical evolution models, this increase is necessary to achieve the Si isotopic ratios of the solar system. If most mainstream SiC grains come from AGE stars that were born within a short time span, local heterogeneities must be the dominant cause of their Si isotopic variations. However, if AGE stars of different masses and therefore different ages contributed SiC to the solar system, the Si distribution of the mainstream grains reflects both the effect of Galactic chemical evolution of the Si isotopes and of isotopic heterogeneity at the time these stars were born.
