ON THE THEORY OF ASTRONOMICAL MASERS IN 3 DIMENSIONS

In the standard theory of three-dimensional astronomical masers, the radiation field is described as if the source were comprised of a collection of linear masers, an approximation that has been justified by the highly beamed nature of the radiation. Recently, Neufeld has noted potential difficulties with this description and has supplied the general expressions for the maser problem without assuming beaming at the outset. The consequences of these general expressions, which have been formulated already in 1973 by Litvak and in 1974 by Bettwieser & Kegel, are analyzed here. To leading order, the standard theory is shown to provide the correct description of three-dimensional masers and its results remain intact, but only within a frequency core whose half-width is x(s)DELTAnu(D), where DELTAnu(D) is the Doppler width and x(s) is a dimensionless parameter. For any given geometry, x(s) is approximately 1/theta(sat) where theta(sat) is the beaming angle of a maser with that geometry that has just saturated. For typical pumping schemes, x(s) is approximately 2 in spherical masers, approximately 2.5-3 in disk masers, and approximately 3-5 in cylindrical masers. For frequencies outside this core region, maser operation corresponds to a mode that will be called suppressed, and the standard theory breaks down. In this frequency domain, interaction with core rays that are slightly slanted to the direction of propagation suppresses photon production. In contrast with the core region, in the suppressed regime the rate of maser photon generation never reaches the maximum allowed by the pump processes; this regime effectively corresponds to a maser whose inherent strength is weaker than that of a linear maser whose properties are otherwise identical. Observed maser radiation is effectively confined to the core region since frequencies in a suppressed domain are practically unobservable. In essence, x(s) provides an effective cutoff, defining a width at zero intensity that depends on the geometry but is unaffected by growth at line center. In practice, suppression affects only extreme maser outbursts. Their profiles change in such a way that when fitted with a Gaussian, the linewidth decreases when the line center intensity increases, even for masers that are saturated at the line core-in marked contrast with the predictions of standard analysis of maser linewidths. This behavior could perhaps be related to the inverse relationship between intensity and line width displayed in some intense H2O maser flares in star forming regions.