Interferometric observations of non-maser SiO emission from circumstellar envelopes of AGB stars: Acceleration regions and SiO depletion

We have obtained high (3″-4″) and medium (7″-9″) resolution images of the SiO J = 2-1 (V=0) emission from the circumstellar envelopes (CSEs) of three oxygen-rich Mira variables, χ Cyg, RX Boo, and IK Tau. The SiO images are roughly circular, implying that the CSEs are largely spherically symmetric on angular-size scales of ≈3″-9″. The emission is strongly centrally peaked, but shows a non-negligible amount of extended, low surface-brightness emission. The intrinsic SiO brightness distribution, as a function of radius, is best approximated by a power-law, rather than a Gaussian or exponential function, for our sources. The observed angular half-maximum intensity source radius is nearly independent of LSR velocity for all three CSEs. This behavior is a characteristic feature of power-law distributions, which are scale-free, rather than Gaussian or exponential ones, which have well-defined scale sizes. Detailed radiative transfer/excitation calculations, coupled with a kinematic model of gas acceleration by radiation pressure on dust grains have been used to successfully reproduce the characteristic properties of the observed SiO emission. We find that the emission can be understood using normal radial acceleration models, i.e., those in which the outflow velocity reaches half its terminal value within about 10 stellar radii. Very large-scale acceleration (up to ≈100 stellar radii) is not required, contrary to a recent model proposed by Lucas et al. [A&A, 262, 491 (1992)]. In χ Cyg and RX Boo, the line-profiles are rounded, typical of optically-thick emission from a spherical envelope expanding with a constant velocity. The presence of an additional (kinematically) narrower central component in the line profiles observed toward IK Tau (both with high and medium resolution observations), implies the existence of an inner circumstellar shell with a significantly smaller expansion velocity than the extended envelope. The radial distribution of the SiO abundance, from small (10¹⁵ cm) to large radii (> 10¹⁶ cm), is constrained by the observed half-maximum intensity source sizes, and ratios of the source fluxes in small and large beams. We find that a rapid depletion of SiO from the gas phase must occur at radii larger than about (1-2) 10¹⁵ cm, initially by the process of adhesion onto dust grains, followed by photodissociation by the interstellar UV. IK Tau has a higher average fraction (by a factor 2.7) of SiO left over in the extended envelope, as compared to χ Cyg and RX Boo, which are similar in this respect. Depending on the stellar mass-loss rates and distances, the initial SiO abundance in the circumstellar envelopes of IK Tau, χ Cyg, and RX Boo, is about (1-few) 10^-5.