The amplification of celestial maser radiation in the general many-level case

We have developed a theoretical framework which can in principle be used for the interpretation of observational data for cosmic masers of all types (e.g. OH, H2O, SiO, CH3OH, megamasers). Our main concern is with the description of the transport of maser radiation and we present a semi-classical formulation of maser saturation in many-level systems in which many masers may propagate simultaneously. Building upon results obtained in earlier semiclassical theories for two- and four-level systems, we include the full coupling between the kinetic model for the maser inversion pump and the saturating effects of maser radiation. We explicitly solve the generalized Bloch equations in the steady state to yield a formula for level populations which depend on the intensities of all masers present in the medium as well as upon the details of the kinetic model. These populations are then coupled to a set of exponential gain equations whose solution yields a set of maser intensities as a function of gain length. In order to illustrate the type of prediction which this theory provides, we perform a few sample calculations relevant to star-forming regions for OH masers with a model involving 36 hyperfine levels. Since there are in general many inversions, we find that more than 20 masers may propagate simultaneously, although only a very few are predicted to achieve sufficient intensity to be observable. In order to compare the predictions of this theory usefully with observations we require data for maser regions in which intensities at several frequencies have been recorded for each maser spot. Such data are increasingly becoming available and we intend in future to work to compare observed intensities in the 18cm (⁠|$J=1\frac 12$|⁠), 6cm(⁠|$J=\frac 12$)| and 5 cm (⁠|$J=2\frac 12$|⁠) groups of lines with our predicted values, to establish with more confidence than hitherto the physical conditions appropriate to the observed maser action.