Numerical simulations of stellar SiO maser variability: Investigation of the effect of shocks

A stellar hydrodynamic pulsation model has been combined with a SiO maser model in an attempt to calculate the temporal variability of SiO maser emission in the circumstellar envelope (CE) of a model AGB star. This study investigates whether the variations in local physical conditions brought about by shocks are the predominant contributing factor to SiO maser variability because, in this work, the radiative part of the pump is constant. We nd that some aspects of the variability are not consistent with a pump provided by shock-enhanced collisions alone. In these simulations, gas parcels of relatively enhanced SiO abundance are distributed in a model CE by a Monte Carlo method, at a single epoch of the stellar cycle. From this epoch on, Lagrangian motions of individual parcels are calculated according to the velocity elds encountered in the model CE during the stellar pulsation cycle. The potentially masing gas parcels therefore experience dierent densities and temperatures, and have varying line-of-sight velocity gradients throughout the stellar cycle, which may or may not be suitable to produce maser emission. At each epoch (separated by 16.6 days), emission lines from the parcels are combined to produce synthetic spectra and VLBI-type images. We report here the results for v =1 ,J = 1{0 (43-GHz) and J = 2{1 (86-GHz) masers and compare synthetic lineshapes and images with those observed. Strong SiO maser emission is calculated to form in an unlled ring within a few stellar radii of the photosphere, indicating a tangential amplication process. The diameter of the synthetic maser ring is dependent upon stellar phase, as clearly observed for TX Cam, and upon maser transition. Proper motions of brightly masing parcels are comparable to measurements for some maser components in R Aqr and TX Cam, although we are unable to reproduce all of the observed motions. Synthetic lineshapes peak at the stellar velocity, have typical Mira linewidths and vary in intensity with stellar phase. However, the model fails quantitatively in several respects. We attribute these failings to (i) lack of an accurate, time-varying stellar IR eld (ii) post-shock kinetic temperatures which are too high, due to the cooling function included in our model and (iii) the lack of a detailed treatment of the chemistry of the inner CE. We expect the use of oxygen-rich hydrodynamical stellar models which are currently under development to alleviate these problems.