Hydrogen masers .1. Theory and prospects

The discovery of the first high-gain hydrogen recombination line (HRL) maser in the millimeter/submillimeter spectrum of the emission-line star MWC 349A requires an expansion of current paradigms about HRLs. In this paper we reexamine the problem of non-LTE populations in recombining hydrogen and specify the conditions necessary for high-gain masing and lasing in HRLs. To do so, we use the extensive new results on hydrogen level populations produced by Storey & Hummer and our calculations for the net (that is, line plus continuum) absorption coefficient for HRLs. We present results for the alpha- and beta-lines whose principal quantum numbers n are between five and 100, for gas whose electron number density 3 less than or equal to log N-e(cm(-3))less than or equal to 11, at two electron temperatures, T-e = 5000 and 10,000 K. We show that the unsaturated maser gain in an HRL is a sharp function of N-e, and thus to achieve high-gain masing, each line requires a sufficiently extended region over which the density is rather closely specified. Saturation of masing recombination lines is a critical consideration. We derive a simple equation for estimating the degree of saturation from the observed flux density and the interferometric and/or model information about the amplification path length, avoiding the vague issue of the solid angle of masing. We also present a qualitative way to approach the effects of saturation on adjacent emission lines, although the detailed modeling is highly case-specific. We draw attention to another non-LTE phenomenon active in hydrogen: the overcooling of populations. This occurs for HRLs with n greater than or similar to 20, in gas where N-e less than or similar to 10(5) cm(-3). Observationally, the HRL overcooling might manifest itself as an anomalously weak emission recombination line, or as a ''dasar,'' that is, an anomalously strong absorption line. In the simplest case of a homogeneous H rr region, the absorption can be observed on the proper free-free continuum of the region, if some conditions for the line or/and continuum optical depths are satisfied. We briefly discuss the prospects of detecting hydrogen masers, lasers, and dasars in several classes of Galactic and extragalactic objects, including compact H II regions, Be or Wolf-Rayet stars, starburst galaxies, and active galactic nuclei.