4 Discussion

4.1 Periodicities and detached shells

Cyclic variations in the OH mainline emission were found for the three semiregular variables. The OH period inferred for W Hya, which is classified as SRa star, agrees very well with the optical period (Kholopov et al. 1985). In contrast, both SRb stars, R Crt and RT Vir have two OH periods (determined from the most sampled intervals of data) which differ from the optical periods given by Kholopov et al. (1985). This discrepancy is likely to be due to the scarcity of the optical data for both objects, but multi-periodic variations of OH masers can also have non-trivial causes. We note sub-cycles in the variability of all three stars. These resemble the bumps usually observed in the optical and OH variability curves of classical Miras (Etoka 1996; Etoka & Le Squeren 2000) but these are more prominent in the semiregulars. The bumps and the long-term variations over several cycles may be related to the dust formation mechanism. Winters et al. (1994) have shown that, taking into account the dynamic structure of the dust shell, secondary maxima are produced in light curves at wavelengths longer than 2.2 $\mu$m as an effect of the thermal emission contribution of newly formed dust layers in the most inner part of the circumstellar shell.

As noted in Sect. 3.2, emission from W Hya near 46.5 km s^-1is transient but can be bright. We suggest this comes from the red-shifted parts of a detached shell, the blue-shifted parts of which possibly produce the emission near 33.8 km s^-1. Phase-lag measurements (Sect. 3.4) indicate that this feature arises at a greater distance from the star than the rest of the blue-shifted OH mainline emission but which is typical for 1612 MHz emission. Such detached shells could result from the super-periodicities in dust formation predicted by Winters et al. (1994).

Gómez Balboa & Lépine (1986) studied the integrated flux variations of the 22 GHz maser emission of late-type stars including R Crt and W Hya from 1976 August to 1982 February. They observed aperiodic variations in the H₂O maser emission of R Crt which span several cycles. W Hya showed super-periodic behaviour on timescales which were multiples of the fundamental period. We note that OH maser behaviour observed by us is quite similar to that reported for the water masers.

4.2 Peculiar behaviour

In contrast to the long term behaviour of the integrated flux of Miras (Etoka 1996; Etoka & Le Squeren 2000), variations in the integrated OH flux density of the semiregulars are quite large, up to a factor 10 during less than 600 days. Erratic behaviour of the OH mainlines is expected from theoretical calculations as an effect of transient instabilities in hotter and less dense regions of the envelope with low optical depth (Elitzur 1978). We documented well a few features which exhibit a flaring behaviour. The relationship between their linewidths and peak flux densities suggests that unsaturated amplification operate in some clouds of the OH envelope. This possibility is strongly supported by temporal variations of their peak fluxes uncorrelated with the total intensities. There are other examples of such behaviour, but with our spectral resolution we cannot be sure whether an effect of line narrowing or re-broadening is mimicked by blending. Observations at higher spectral resolution and high angular resolution should be useful to eliminate possible blending of features.

The appearance of a very blue-shifted feature at 1667 MHz in W Hya, which makes the profile deviate from a standard double-peaked shape, possibly reflects a global change in excitation conditions of the maser envelope. This outermost feature is likely to emerge from an old OH envelope possibly excited by the central source as observed at 1667 MHz in U Her (Sivagnanam et al. 1989). Detection of faint emission at 1612 MHz from the same source is consistent with the view that in the outer parts of the maser envelope, favourable conditions just occurred. No 1612 MHz emission was detected towards R Crt and RT Vir, which is certainly due to a thinner circumstellar shell for these SRb stars. This is consistent with the interferometric data (Szymczak et al. 1999) for R Crt.

4.3 Tangential amplification

Although the OH profiles of the studied semiregulars are far from classical, most of the OH emission appears to be beamed along radial paths. Weak emission at velocities very close to the systemic velocity occurred during some time intervals in R Crt and RT Vir, and almost always in W Hya as an effect of tangential beaming. In R Crt and RT Vir, the appearance of tangential emission usually coincides with a high level of total OH emission. In W Hya, the 1667 MHz emission at the systemic velocity usually follows the total emission, while the 1665 MHz emission is random and less stable than the radial emission. We note that the tangential emission of the OH semiregulars occurs preferentially during the periods of high maser activity in the envelopes. Tangential beaming requires a maser shell of sufficient width, or at least containing clumps of sufficient sizes to supply sufficient column densities for maser amplification.

In December 1995 an interferometric observation of R Crt with a high angular resolution was made (Szymczak et al. 1999) and the brightest peaks at 1665 and 1667 MHz had brightness temperatures greated than $3\times 10^6$ and $5\times 10^6$ K, respectively. No tangential emission was detected during that observation. Fortunately, at both mainlines during $1650< {\rm JD}_{\rm m}<1850$ when tangential emission was present, the level of radial emission was the same as during interferometric measurements. In extrapolating the above brightness temperatures to that epoch some useful information can be inferred from the observed properties of tangential radiation. At the epoch considered, the peak flux ratios of the tangential to the radial emission were 0.16 and 0.04 at 1665 and 1667 MHz, respectively. Assuming that tangential emission does not come from a complete ring-like structure but rather from a single cloud, those ratios allow to evaluate the brightness temperatures of tangential emission in both mainlines. This assumption about the structure of the tangential emission is well supported by the simple unblended shape of the feature identified as tangential emission for both R Crt and RT Vir. There is also another well known source VX Sgr in which OH emission near the systemic velocity comes from a single cloud (Szymczak & Cohen 1997). However this does not appear to be the case for W Hya as OH emission at close $v_{\rm s}$ is obviously blended and may come from extended structures of low emission which is below the sensitivity limit of modern instruments. For R Crt the brightness temperatures deduced for tangential emission are greater than $5\times 10^5$ and $2\times 10^5$ K at 1665 and 1667 MHz respectively. The standard model of maser amplification (Goldreich & Kwan 1974) predicts that corresponding optical depths $\tau$ are -13.1 and -12.2. As the linewidth of the maser feature narrows by a factor $\sqrt{-\tau}$, then the observed linewidths of 0.24 and 0.26 km s^-1, at 1665 and 1667 MHz respectively, correspond to the thermal linewidths at half maximum $\Delta$v of 0.87 and 0.91 km s^-1. These imply a kinetic temperature in the regions of tangential emission of 290-320 K. R Crt has an OH envelope of radius $R_{\rm OH} = 9\times 10^{14}$ cm (Szymczak et al. 1999), therefore with an expansion velocity of $v_{\rm e}$ = 9 km s^-1, the gain length of the tangential maser is $R_{\rm OH}\Delta v/v_{\rm e} = 9\times 10^{13}$ cm. The lower limit of linewidth of tangential maser emission is about 0.18-0.20 km s^-1. This suggests that when the kinetic temperature drops below 150-200 K, tangential amplification is not longer maintained in the envelope of R Crt. We believe that the gas temperature is an important factor which can influence the tangential amplification at distance below 10¹⁵ cm from the star.

4.4 Evolutionary status of OH semiregulars

Kerschbaum & Hron (1992) deduced that SRa stars are a mixture of "intrinsic Miras'' and SRb stars, this latest group has been divided into two groups: the "blue'' semiregulars with no indication of circumstellar shell and for which optical periods are lower than 150 days and effective temperatures are greater than 3200 K, and the "red'' semiregulars with similar effective temperatures and mass loss rates as Miras but with a period about half as long. Jura & Kleinmann (1992) have inferred similar conclusions. In their classification, W Hya belongs to their first group of semiregulars with optical periods of 300-400 days and is a member of "thin disk'' population of Miras. R Crt and RT Vir with optical periods ranging from 150 to 200 days belong to the third group of semiregulars according to classification scheme of Jura & Kleinmann. This group may have more than one main progenitor population. On the other hand, the mass loss rates of the studied OH semiregulars are about $10^{-7}~M_\odot$ yr^-1 (Kahane & Jura 1994; Loup et al. 1993). This is only slightly lower than those derived for OH Miras (Sivagnanam et al. 1989). Our data support the view that W Hya belongs to Mira population showing OH behaviour different from that of the two SRb stars. The observed bursts and less regular variations of the OH emission of the two SRb stars imply that they have thinner OH envelope than W Hya as a result of recent lower mass loss rates. The OH periodicity (longer than 250  days) determined from our data for R Crt and W Hya together with the OH expansion velocities (7-11 km s^-1) well obey the period - OH velocity relation established for Mira and OH/IR (Sivagnanam et al. 1989). This suggests that W Hya is as evolved as Miras. Two SRb stars may be either in a Mira-like stage or post-Mira.