Fig. 1 assembles these line fluxes together with previous -line measurements of the source. The mm and submm transitions from to 21 which were previously demonstrated to be masing show up clearly as the high-n part of a bell-shaped hump of increased line flux which stands out above the regularly decreasing (with n) thermal emission. Our ISO data complete the low-n part of this hump which now appears fairly symmetric and smooth. Its quantum number range, peak location and amplitude can now be derived for the first time with some precision.
Arguments that the millimeter transitions in the hump () are masers are based on the following evidence: (i) the high flux densities in the maser spikes and their high line/continuum ratio (Martín-Pintado et al. 1989a), (ii) their strong time variability (Martín-Pintado et al. 1989b; Thum et al. 1992), (iii) their low line ratios (Gordon 1994; Thum et al. 1995), and (iv) theoretical expectation of strong negative line absorption coefficients in a dense ionized wind (Walmsley 1990). In the submm regime, where the line profiles remain similar, but the line fluxes are much higher still than those at mm wavelengths, the -line s must also be masing. At ISO wavelengths where the lines are not resolved we use the velocity-integrated line flux . It exhibits an excess above the smoothly decreasing thermal emission, continuing the trend from the submm/mm masers into the infrared.
The dotted line in Fig. 1 describes the prediction of recombination theory (Storey and Hummer 1995) normalized near the non-masing H and, at wavelengths longer than m, corrected for free-free continuum opacity (dash-dotted). It fits the observations outside the laser/maser hump well with the exception of . These line fluxes vary as (dashed line), considerably steeper than the prediction by recombination theory based on optically thin, spontaneous emission. This is evidence that the -line s are at least partially optically thick for , a conclusion reached already previously for H (Thompson et al. 1977) and Br (Hamann and Simon 1986). Our observation that all transitions between and 15 are stronger than extrapolated from these optically thick -line s, supports the argument that the IR lines in the hump are amplified.
A further, more direct argument is based on the flux ratio of - and -line s. The continuous line in Fig. 2 is the prediction of this ratio by recombination line theory for the situation where both transitions originate from the same upper level. The measured ratios show that physical conditions in the gas depart from pure recombination at all n. The sense of the departure for is compatible with the -lines being optically thick. Above the measured ratios fall consistently below the continuous line which describes optically thin emission. This behavior follows if the lines are amplified. Since the absolute value of the absorption coefficient is always higher for the -line s (Strelnitski et al. 1996b), they are amplified more and .
We conclude that all -line s in the line-excess hump are amplified, including those from to 15 at ISO wavelengths. These transitions are thus infrared lasers, and MWC 349 is the first known source (Strelnitski et al. 1996a) of astronomical lasers.
3.2. A simple model
Normalization of the line fluxes by this first order thermal model shows the laser/maser hump in greater detail (Fig. 3), in particular its quantum number range (from to ) and its peak at where the amplification is . These observed properties can be understood from tables of the hydrogen recombination line absorption coefficient as a function of n and electron density (Walmsley 1990; Storey and Hummer 1995). For increasing the quantum number range where is negative, and hence masing is possible, gradually shifts towards smaller n. The resulting behavior of is concisely summarized in Fig. 8 of Strelnitski et al. (1996b), which shows that amplification peaks at the measured for cm-3. We take this to constitute the maximum in the source, in accordance with an investigation of its Paschen decrement (Thum and Greve 1997). Lower density components must also be present, however, since the level inversion rapidly decreases for in a cm-3 plasma and ceases altogether near , at variance with the observation. These lower components may also generate masers in their specific quantum number ranges which are shifted to .
For a more quantitative understanding of the resulting amplification pattern we investigated the simple model of a linear maser of total length L, which consists of an unsaturated core and surrounding saturated zones. Following the formalism developped by Elitzur (1992) maser growth is exponential in the core, but linear in the saturated zones. From the range of available , the model maser selects for each n the optimum where is largest (Strelnitski et al. 1996b). Varying the only two free parameters, L and the optical depth of maser saturation , we obtain a reasonable fit to the observed amplification pattern (Fig. 3) for a.u. and as long as . The higher n masers require progressively longer paths, up to at . We therefore propose a simple picture where the lasers/masers all propagate along similar paths roughly parallel to the disk surface, probably somewhat interior to the H maser at a.u. from the center (Planesas et al. 1992). The masers are probably located further out on the disk where is lower and longer paths are geometrically possible. The outer disk radius, a.u. (White and Becker 1985), is of the order of suggesting that the size of the disk limits the quantum number range of the maser at large n by limiting the maser gain.
At the other end of the quantum number range the transition between optically thick thermal line emission and amplification is very sharp at , only slightly higher than the case B prediction () for a cm-3 plasma. While H photons are still trapped in the disk plasma and help to thermalize the level populations, H photons may escape, possibly in the vertical direction, thus driving the level populations towards case B, i.e. inversion.
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998