P. te Lintel Hekkert, A.A. Zijlstra, J.M. Chapman, L. Likkel, J.R. Cohen and R.P. Norris
Working hypothesis
In the working model, we assume that asymmetries develop during the phase of high mass loss which terminates the AGB. Most AGB stars show significant polarization in the infrared (Johnson and Jones 1992), which points to asymmetries near the star. Although, there is insufficient evidence to conclude that earlier mass-loss gives rise to non-spherical shells, observations in this paper of UX Cyg would be consistent with the scenario that envelop asymmetries observed in the Post-AGB phase have their origin in the early AGB phase. We assume that during the last phase on the AGB a torus of material is formed, either due to preferential mass loss in the equatorial plane or due to a hydrodynamical interaction of the (spherical) stellar wind with asymmetrical distributed matter deposited during earlier (non-spherical) mass loss episodes. The working model consists of four elements: an increasingly hot star, with an increasingly faster (hot) stellar wind. The latter is collimated by a torus of cold material (about 100K) and send into the AGB remnant, which has now formed two bubbles or lobes at either side of the torus. This working model is a simplified version of what is seen in most planetary nebulae. All our observations of the OH masers in the post-AGB objects in the present sample are consistent with the idea that the maser emission originates from the inner interaction zone between the fast stellar wind and the AGB remnant. Thus, in our working model the OH emission originates in two parts. Firstly, inside the slowly expanding torus. Secondly, in the interface between the fast wind and the AGB remnant. The latter interface corresponds to the inner edge of the bubble. An important aspect of post-AGB shells is that the OH-emitting layers are thin. This is in contrast to the OH/IR star phase, when the masing shell is very thick. Consequently, most of the maser emission will be unsaturated. Further, instead of the 1612MHz the 1667 MHz transition will generally dominate although both the 1612MHz and 1665MHz emission will be present (Field 1987). Further, the spectral profile becomes more irregular since the maser emission will exponentially amplify small density enhancements (clumps). As some of these clumps have magnetic fields embedded in them (Cohen .....), high degrees of polarization will exist. Finally, since the strongest maser emission will be seen to originate from the longest path lengths, in thin shell maser regions, the tangential maser (wrt the envelope) will dominate, similar to what is seen in SiO masers (Diamond 1994). In such a system, the maser process has a random component, following small changes in density. It is therefore very likely that only a part of the entire structure will show up in images of the maser.
The observations
We observed most of the sources in our sample with VLA in A/B hybrid configuration. The sources were observed simultaneously in left-circular and right-circular polarization, with integration times of a few minutes. For southerly objects at low declination, the hybrid array gives a more circular beam.
Expansion diagrams
Interpreting the data cubes is difficult, for two reasons. The cubes are a three-dimensional projection of a six-dimensional structure (position and velocity vectors). Parts of the structure may be hidden because they do not mase in our direction: the sampling is not complete. In order to simplify the interpretation, we reduce the cube to a two-dimensional representation. First, a point of symmetry is defined. Second, we calculate the projeted distance of each emission component to this point of symmetry and we plot the velocity against this distance. The emission components are defined from gaussian fitting. This has been found to be very efficient for compact maser components: their centroid can be accurately determined to typically a tenth of a pixel. For extended emission at low surface brightness, this procedure does not work and we therefore do not make use of all the data. However, only for two sources do miss a major fraction of the emission in this way (OH349 and He3-1475). Most structures we expect to find in our sources (as implicit in our working model) are reduced to simple lines and curves if the correct point of symmetry is chosen. We therefore iterate to find a symmetry point which reduces the position-offset--velocity diagram (which we will call {\it expansion diagram} to a collection of such structures. In general this will be the case if the chosen point lies on a projected line of symmetry of the structure; e.g., for a toroidal ring seen under a certain inclination, a point lying on the major axis of the observed ellipsoid should be chosen. The projected toroidal, expanding ring gives rise to curved structures in the expansion diagram. In contrast, material along the edge of the lobes shows up as a straight line: this was first shown by Shu et al. (...) for bipolar lobes around young stellar objects. A possible cm\omplication is that these different structures may require different points of symmetry to show up. We will not use this, and choose one point per source. The Figure show the expansion diagrams for OH231.8+4.2. It shows that the deformed circle is in fact the ring which correspond to the inner torus. The component which is left is the straight line. This we compare with the Shu model and conclude: fantastic exactly hat one would expect, but then ballistic,