We investigate the formation of silicon carbide ( SiC ) grains in the framework of 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 size distribution .
Two cases are considered for the nucleation process ; one is the LTE case where the vibration temperature of SiC clusters T _ { v } is equal to the gas temperature as usual , and another is the non–LTE case in which T _ { v } is assumed to be the same as the temperature of small SiC grains .
The results of hydrodynamical calculations for a model with stellar parameters of mass M _ { \ast } =1.0 M _ { \odot } , luminosity L _ { \ast } =10 ^ { 4 } L _ { \odot } , effective temperature T _ { eff } =2600 K , C/O ratio=1.4 , and pulsation period P =650 days show the followings : In the LTE case , SiC grains condense in accelerated outflowing gas after the formation of carbon grains and the resulting averaged mass ratio of SiC to carbon grains of \sim 10 ^ { -8 } is too small to reproduce the value of 0.01–0.3 inferred from the radiative transfer models .
On the other hand , in the non–LTE case , the formation region of SiC grains is inner than and/or almost identical to that of carbon grains due to the so–called inverse greenhouse effect .
The mass ratio of SiC to carbon grains averaged at the outer boundary ranges from 0.098 to 0.23 for the sticking probability \alpha _ { s } =0.1–1.0 .
The size distributions with the peak at \sim 0.2–0.3 \mu m in radius cover the range of size derived from the analysis of presolar SiC grains .
Thus the difference between temperatures of small cluster and gas plays a crucial role in the formation process of SiC grains around C–rich AGB stars , and this aspect should be explored for the formation process of dust grains in astrophysical environments .