The circumstellar envelopes (CSEs) around late-type stars contain several maser species that are excellent probes of the dynamics of the outflowing material. Astrometric observations are an important tool to study the locations and motions of the circumstellar masers with respect to the central star. This understanding is essential to reach the main goal of maser astrometry, which is to determine the distances to heavily enshrouded stars, that are too faint for their parallax to be determined directly.
Interferometric observations of the 22 GHz H2O masers in the CSEs of Mira-variable stars with MERLIN, the VLA and Very Long Baseline Interferometry (VLBI) indicate that the H2O masers are found up to a few hundred AU from the star (e.g. Lane et al. 1987). This is generally inside the OH maser shell, which is located at up to several 1000 AU. The H2O masers often show an a-spherical distribution, and the size of the maser region is thought to increase with mass-loss rate (Cooke & Elitzur 1985). The maser is expected to be pumped due to collisions (Neufeld & Melnick 1991). The 22 GHz maser can then be easily excited in the inner parts of the CSE at temperatures of 400 to 1000 K and H2 number densities of 109 cm-3. In this region the outflow is still being accelerated. Therefore, as shown by Rosen et al. (1978) the velocity coherent paths through the masing medium are of approximately equal length in both the radial direction as well as the direction tangential to the star, and thus the H2O maser beaming is expected to be both radial and tangential. The radial beaming results in the maser occurring in front of the star, tangential beaming would display a ring within a narrow velocity range close to the stellar velocity (e.g. Reid & Menten 1990).
H2O masers are significantly more variable than their OH cousins. They exhibit strong variability in intensity, which seems to indicate that the masers are at least partially unsaturated, since an unsaturated maser is strongly influenced by changes in the local conditions. An analysis of the H2O maser line-widths and line-shapes also indicates that the masers are not completely saturated (e.g. Vlemmings et al. 2002).
Whereas semi-regular stars are observed to have H2O maser spectra that can change shape rapidly, Mira-variable stars typically show no large profile changes over several years. However, the individual features can still show significant changes in intensity (Engels et al. 1988).
Interferometric observations of OH masers have revealed that the most compact features were only found at the blue-shifted side of the spectrum (Norris et al. 1984). It was argued that this was due to amplification of the continuum maser emission from the underlying star by the maser screen in front of it. This is called the Amplified Stellar Image Theory. Amplification of the stellar emission results in a high brightness maser spot at the most blue-shifted side of the OH maser spectrum. This spot should coincide at the different OH maser transitions, and is expected to be persistent over a long period of time. Several observations have confirmed this hypothesis (e.g. Sivagnanam et al. 1990).
According to the amplified stellar image theory, the compact, most
blue-shifted, spot is necessarily fixed to the stellar position.
Therefore, high resolution astrometric observations of this spot can
be used to determine the stellar trajectory. This hypothesis has been
tested for the Mira-variable star U Her by van Langevelde et al. (2002, hereafter vL00). The absolute positions of the OH maser
spots were determined with respect to the radio-reference frame using
extra-galactic phase reference sources. The positions were compared
with the optical Hipparcos positions with unprecedented
accuracy. It was shown that the most blue-shifted spot was indeed
located in front of the stellar radio-photosphere. The size of this
spot was found to be 
20 mas, which is comparable with the
expected size of the radio-photosphere, which is thought to be twice
the size of the star, as proposed by Reid & Menten (1997).
Although the H2O masers generally show a great number of spots over an area of several hundred mas, it has been argued that in some cases one of the H2O maser spots corresponds to the stellar image (Reid & Menten 1990; Marvel 1996; Colomer et al. 2000). However, because the distribution of the H2O masers is considerably less spherical than that of the OH masers, it is not straightforward to assume that the stellar image underlies the most blue-shifted spot. Also, because the maser brightness depends strongly on local effects such as density or pumping inhomogeneities, several bright spots can be observed and an H2O maser stellar image could be less conspicuous or persistent than the OH stellar image.
Here we present phase referencing observations of the H2O masers around U Her used to determine accurate maser spot positions. These have been compared with the Hipparcos optical position and the positions obtained for the OH masers in vL00.
Copyright ESO 2002