Non-local radiative transfer of SiO masers in Miras

Context. To properly understand the propagation of SiO masers within the shocked region of the circumstellar envelope of asymptotic giant branch stars, non-local radiative transfer calculations are required. Aims. The present study focuses on investigating how the non-linear velocity field affects the amplification of SiO masers in the circumstellar envelope of a Mira variable. Methods. We extend the capability of the coupled escape probability method to a spherical system and develop subroutines that are able to calculate the radiative transfer problems in an arbitrary velocity field. This method is applied to the model of a Mira variable that shows dramatic fluctuations in its physical conditions in the circumstellar envelope. We carry out the non-local calculations over the subset of whole epochs covering a complete stellar-pulsation cycle. We also include maser saturation in our calculations to properly treat the interaction of SiO maser radiation with the SiO molecules. Results. We reproduce the typical features of SiO masers in Mira variables and compare our results with previous large velocity gradient (LVG) calculations and observations. The region of SiO masers is very confined, at a distance of about one stellar radius from the photosphere, which implies that there has been a tangential amplification process. The relative strengths and positions of SiO masers of v = 1, J = 1−0,2−1 and v = 2, J = 1−0 transitions are shown. The temporal variability of a SiO maser, which is driven by stellar pulsations, is also examined in this study, and our results show some differences from those of previous LVG calculations