| Abstract
| - Context. The nature of maser emission means that the apparent angular size of an individual maser spot is determined by the local amplification process as well as by the instrinsic size of the emitting cloud. Highly sensitive radio interferometry images made using MERLIN spatially and spectrally resolve water maser clouds around evolved stars. Aims. We used measurements of the cloud properties, around the red supergiant S Per and the AGB stars IK Tau, RT Vir, U Her and U Ori, to test maser beaming theory. In particular, spherical clouds are expected to produce an inverse relationship between maser intensity and apparent size, which would not be seen from very elongated (cylindrical or slab-like) regions. Methods. We analysed the measured properties of the maser emission in order to estimate the saturation state. We analysed the variation of observed maser spot size with intensity and across the spectral line profiles. Results. Circumstellar masers emanate from discrete clouds from about one to 20 AU in diameter depending on the star. Most of the maser features have negative excitation temperatures close to zero and modest optical depths, showing that they are mainly unsaturated. Around S Per and (at most epochs) RT Vir and IK Tau, the maser component size shrinks with increasing intensity, although in some cases the slope is shallower than predicted, probably due to shape irregularities and the presence of velocity gradients within clouds. In contrast, the masers around U Ori and U Her tend to increase in size, with a larger scatter. Conclusions. The water masers from S Per, RT Vir and IK Tau are mainly beamed into spots with an observed angular size much smaller than the emitting clouds. The brighter spots at the line peaks are smaller than those in the wings. This suggests that the masers are amplification-bounded, emanating from clouds which can be approximated as spheres. Many of the masers around U Her and U Ori have apparent sizes which are more similar to the emitting clouds and have less or no dependence on intensity, which suggests that these masers are matter-bounded. This is consistent with an origin in flattened clouds and these two stars have shown other behaviour indicating the presence of shocks which could produce this effect.
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