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We investigate the formation of silicon carbide (SiC) grains in the frameworkof dust-driven wind around pulsating carbon-rich Asymptotic Giant Branch(C-rich AGB) stars in order to reveal not only the amount but also the sizedistribution. Two cases are considered for the nucleation process; one is theLTE case where the vibration temperature of SiC clusters $T_{\rm v}$ is equalto the gas temperature as usual, and another is the non-LTE case in which$T_{\rm v}$ is assumed to be the same as the temperature of small SiC grains.The results of hydrodynamical calculations for a model with stellar parametersof mass $M_{\ast}$=1.0 $M_{\odot}$, luminosity $L_{\ast}$=10$^{4}$ $L_{\odot}$,effective temperature $T_{\rm eff}$=2600 K, C/O ratio=1.4, and pulsation period$P$=650 days show the followings: In the LTE case, SiC grains condense inaccelerated outflowing gas after the formation of carbon grains and theresulting averaged mass ratio of SiC to carbon grains of $\sim$ 10$^{-8}$ istoo small to reproduce the value of 0.01-0.3 inferred from the radiativetransfer models. On the other hand, in the non-LTE case, the formation regionof SiC grains is inner than and/or almost identical to that of carbon grainsdue to the so-called inverse greenhouse effect. The mass ratio of SiC to carbongrains averaged at the outer boundary ranges from 0.098 to 0.23 for thesticking probability $\alpha_{\rm s}$=0.1-1.0. The size distributions with thepeak at $\sim$ 0.2-0.3 $\rm{\mu}$m in radius cover the range of size derivedfrom the analysis of presolar SiC grains. Thus the difference betweentemperatures of small cluster and gas plays a crucial role in the formationprocess of SiC grains around C-rich AGB stars, and this aspect should beexplored for the formation process of dust grains in astrophysicalenvironments.

Formation of SiC Grains in Pulsation-Enhanced Dust-Driven Wind Around Carbon Rich Asymptotic Giant Branch Stars