7 Classification of stellar $\mathsf{H_{2}}$O masers

The spatial structure and temporal variability of the observed and predicted stellar H₂O masers fall into three groups, broadly characterised by the energy of the upper level, $E_{\rm u}$, of their transitions.

7.1 Group I: masers typically of $\mathsfsl{E_{u}> 950}$ K

In the CE model, these masers are calculated to be similar in spatial structure to the 321GHz maser, see Fig. 6. The strongest emission occurs in a single dominant region, mostly within 5.5 R_* of the model star. This category includes the 906, 1296, 1322 (an exception as it has $E_{\rm u} = 796$ K), 1441, 1766, 2245, 2532 and 2575GHz masers. These masers have a very restricted range of possible pumping conditions in the circumstellar environment and occur in regions close to the star, in regions of high gas density and dense stellar radiation field. In Group I masers, the total maser flux observed towards the source depends on a small number of very bright masers, rather than a large number of weaker components. Only a small percentage of maser sites produce emission in the line-of-sight, typically <20$\%$ of the initial Monte Carlo sample. The maximum velocity-averaged flux of a maser spot in these transitions is larger than that of masers from Group II and III in general by 1-2 orders of magnitude respectively. If the physical conditions at only a few maser sites change such that emission at these sites is significantly weakened, this will have a dramatic effect on total maser brightness observed towards the source. These masers also are located in the innermost region of the CE, the region most affected by the passage of shocks. It is therefore expected that these masers will have the most dramatic temporal variability of the stellar H₂O masers, as observed for 321GHz masers by Yates & Cohen (1996).

7.2 Group II: masers of 450 K $\mathsfsl{< E_{u}< 950}$ K

These masers resemble the 22GHz and 325GHz masers. They tend to have radial emission distributions which peak at around 3 and 7  R_* in the CE model, see Fig. 9. These are the 970 and 1158GHz masers. These masers have upper transition levels in the range 450-950 K and are pumped out to regions of lower density and of a more diluted stellar radiation field than the masers in Group I. The number of maser components calculated to emit in the line-of-sight is $\ge$25$\%$ and less than 50$\%$ of the possible total. The maximum averaged flux of the spots is moderate relative to that in Group I. The relatively large number of sites, extending over a large region of the CE, suggests that the loss of maser emission from a few sites is not likely to have a significant effect on the total maser output from the source. Also, maser components exist both within and outside of the region most disrupted by shocks. These masers are therefore predicted to show a lesser degree of temporal variability than the Group I masers, as observed by Yates & Cohen (1996). Yates & Cohen (1996) also noted that 22 and 325GHz masers do not vary synchronously, however. This could be due to the fact that the peaks in the radial distribution of maser emission are not coincident for the different frequencies. We would expect 22GHz masers to show the effect of a shock wave traversing the CE first, as the maximum in the radial distribution of maser intensity is nearer to the photosphere than that of the 325GHz maser.

7.3 Group III: masers of $\mathsfsl{E_{u}< 450}$ K

The 380GHz and 448GHz masers resemble the 183GHz maser. As for the 183GHz maser, these masers occupy large extents in the CE, with relatively weak emission extending out to radii of 18-27  R_*. It is clear that these masers, which originate from the most low-lying energy levels, can be pumped by regions of much lower density and temperature than their Group I and II counterparts, as well as by the higher temperature and density regime closer to the star. This explains the large number of maser sites producing emission at these frequencies, which is >60$\%$. The maximum averaged component flux in each transition is less than that of the masers in Group II typically by an order of magnitude. As the loss of emission from these transitions at a few sites would not produce a significant effect on the maser output or spatial structure, temporal variability is expected to be the lowest in these masers. This corresponds well to the observational results of González-Alfonso et al. (1998) in which the intensity of 183GHz maser lineshapes appears to remain very stable. However, in stars of similar mass loss rate to our model, the lineshape peak can shift in velocity to either side of V_* between observational epochs. This is also the case for SiO maser lineshapes. We require variability calculations in order to understand this behaviour.