6 Conclusion

The study of the long term behaviour of OH variability of Miras is a powerful tool in the investigation of circumstellar shells under various aspects. This study showed that:

• the optical and OH periods agree within 6%;
• the optical light curves are more strongly asymmetrical than the OH ones, although the shapes of these two variability curves are similar: if there are secondary maxima in the optical curves, they are observed in the OH curve too;
• the delay at maximum in comparison with the optical one is greater in OH than at 10 $\mu$m. Since this delay increases with the wavelength in infrared radiation, the far infrared radiation coming from the dust probably plays an important role in the pumping;
• the values of the OH integrated flux minima and maxima are not correlated with those of the optical curve;
• the values of $\Delta I_{\rm min-max}$ for the integrated flux are usually of about 30 - 35% at 1612 MHz, hardly ever exceeding 50%, while the amplitudes of variations in both main lines are generally greater than 30%, sometimes reaching values as high as 95%;
• the integrated flux at 1612 MHz is clearly more saturated than that of the main lines;
• the curves of the OH integrated flux coming from the front part of the shell are similar for both main lines and are different from the variability curves coming from the back part of the shell;
• the mean value of the integrated flux undergoes a slow modulation during an interval which spreads over several cycles. This is similar to recent studies which have shown that variations over several stellar cycles occur at different levels of the circumstellar shell: in the structure of the ${\rm H_{2}O}$ masers, in the dust formation and in the dynamical structure of the dust shell;
• intermediate peaks (i.e., between the red and blue ones) are only observed in the main lines and do not exhibit particular behaviour either with respect to variability or polarization;
• the degree of polarization for the 1612 MHz standard emission is less than 0.3. Only emission from the standard main line peaks exhibits degrees of polarization as high as 0.6 while inter-peak signal shows zero or very faint polarization. It also appears that the emission at 1667 MHz can be more polarized than at 1665 MHz;
• the observed changes in polarization seem to be related to the variation of the mean integrated flux value;
• the number of components in the 1612 MHz spectral profile is generally less than the number observed in the main lines, moreover the components at 1612 MHz are narrower and exhibit greater longevity;
• the components exhibit cyclic variation in phase with the optical curve if we take into account the usual delay at maximum of about 10 - 20% of the period. Nevertheless, the mean value of the intensity and the amplitude of variations from a cycle to another can differ notably from one group of components to another;
• the OH variations of the most internal component of both standard peaks (taking the stellar velocity as a reference in the spectrum profile), and of the inter-peak emission usually show smaller $\Delta I_{\rm min-max}$ and weaker degree of polarization in comparison with the other components, leading to the hypothesis that they are generally a tangential contribution of the outermost part emitting zones of the concerned line.

Finally, the comparison of the 1612 MHz variations with the main line ones fits with the idea that the 1612 MHz emission is more saturated and comes from of a more external zone than the main lines. Moreover, the behaviour of the OH variations is quite different from one source to another. Thus, some sources show gentle variations, certainly produced by a quite homogeneous envelope, while other sources show more complicated variations which may be due to a more inhomogeneous envelope. But, as revealed by the later interferometric studies and emphasised by the present study, it is apparent that for Miras, inhomegeneous circumstellar envelopes are quite usual. Models must take into account asymmetry even to describe the outermost parts of the circumstellar shell. Thus, Kahane & Jura (1994) needed to introduce a microturbulent velocity dispersion to reproduce their observed CO spectral shapes. The spectra in OH molecule lines also show that velocity field in the envelope is not simple. Differences observed between the variability curves of the red and blue parts of the OH shell as well as the different behaviour observed for the various groups of components belonging to a same peak also clearly show that the evolution of the circumstellar shell is quite complicated and in any case symmetrical.

Acknowledgements

S. Etoka thanks the "Société de Secours des Amis des Sciences'' for financial support through a research grant.