We have performed a thorough study of both radiative and collisional pumping of the SiO masers around late-type stars, carefully considering the combined and separate actions of each type of pump in order to gauge its effectiveness. We find that collisional pumping is severely underestimated when the model calculations use a small number (less than about 18) of rotational levels in each vibrational state. We have developed a procedure that corrects this problem and gives results that are nearly independent of the number of levels utilized in the calculations. We recognize, but do not solve, an important problem that afflicts all escape probability treatments which include maser saturation effects on the level populations. Maser radiation is strongly beamed and the functional form of the beaming angle must be known to properly calculate the maser escape probability. However, the beam pattern for saturated masers in the presence of large velocity gradients has yet to be studied in the literature.
Our model is based on observations and theoretical arguments that place the SiO masers in high-density clumps rather than in the smooth stellar wind. Significantly, general conclusions can be reached which are independent of the pumping mechanism. Most importantly, the overall molecular density is restricted to lie between ~109-1010 cm-3, regardless of the type of pumping. In addition, both collisional and radiative pumps result in the production of a maser chain within each vibrational state, as observed. There are some important differences, however, between the pumping mechanisms. All pumps based on stellar radiation become less efficient with distance from the star because of the rapid decline in pump rate. This prevents any radiative pump from being able to produce the observed maser emission over most of the observed maser region. The only feasible radiative pumps require fine tuning of physical conditions and produce inversion only over a narrow range of optical depths that depends sensitively on the size of the velocity gradient and the form of the escape probability expression. In addition, these radiative pumps have difficulty in explaining the simultaneous production of masers in the same rotational transitions of adjacent vibrational states as is observed. We find that collisional pumping produces the strongest maser emission and, in contrast to radiative pumping, generates maser radiation over the entire observed region and does not require fine tuning of the physical parameters for its operation. Furthermore, there is a significant range of overlapping column densities where collisional pumping produces maser emission in the same rotational transitions of adjacent vibrational states, as observed. Collisional pumping thus appears to be the primary pumping mechanism responsible for the SiO maser phenomenon.
Digital Object Identifier (DOI)
Lockett, Philip B. and Elitzur, Moshe, "Modeling SiO Maser Emission from Late-Type Stars" (1992). Physics and Astronomy Faculty Publications. 228.