3 Results

3.1 Spectral profiles

   

Table 1: Expansion ($v_{\rm e}$) and systemic ($v_{\rm s}$) velocities of the observed SRs

Source	$v_{\rm e}$ (km s-1)		$v_{\rm s}$ (km s-1)	References
	1665 MHz	1667 MHz		for $v_{\rm s}$
R Crt	$9.2\pm06$	$9.2\pm06$	$10.2\pm0.6$	1
W Hya	$5.5\pm0.4$	$6.7\pm0.4$	$40.6\pm0.4$	2
RT Vir	$6.8\pm0.4$	$7.3\pm0.4$	$17.5\pm0.4$	1

1. Wallerstein & Dominy (1988); 2. Neufeld et al. (1996).

The complete atlases of maser spectra of the Stokes parameters I((RHC+LHC)/2) and V((RHC-LHC)/2) of the OH 1667 and 1665 MHz masers of the three sources (Figs. A1-A3) are only available in electronic form.

3.1.1 R Crt

Selected spectra of 1667 and 1665 MHz maser emission from R Crt are shown in Figs. 1 and 2 respectively to illustrate changes in the profile shape. The dates of observations in ${\rm JD}_{\rm m}={\rm JD} - 2~444~950$ are added in parentheses. The maximum velocity extent between the extreme peaks observed allows us to estimate the expansion velocity $v_{\rm e}$ and the systemic velocity (Table 1). In the 1667 and 1665 MHz spectra, three groups of maser features can be distinguished. Two of them, composed of a few blended features, were centred at velocities about 2 and 19 km s^-1. At some epochs the red-shifted emission fell below our detection threshold. Weak 1667 and 1665 MHz emission sometimes appeared in the central velocity range from 8 to 13 km s^-1. The group of red-shifted features centred at $v_{\rm LSR}=19$ km s^-1was strongly circularly polarised in both mainlines and sometimes fully polarised features were observed. Complex spectra in Stokes V were observed for the blue-shifted emission in both mainlines. The circular polarisation of the maser features observed at the central velocities (8-13 km s^-1) was usually weak. Our observations revealed no 1612 MHz emission above the $3\sigma$ upper limit of 0.20 Jy. A tentative detection of this line in 1971 November was mentioned by Dickinson et al. (1973).

Figure 1: Selected spectra of the OH 1667 MHz maser emission from R Crt in a) Stokes I and b) Stokes V taken from 1982 January to 1995 November. The flux density scale is shown by the vertical bar. JD$_{\rm m}$ dates are given in parentheses.

Figure 2: Same as Fig. 1, but for the OH 1665 MHz maser emission.

3.1.2 W Hya

A selection of the OH mainline maser profiles from W Hya are shown in Figs. 3 and 4. The 1667 MHz profile had two emission complexes in the velocity ranges 33-38 and 42-48 km s^-1, each consisting of 5-9 blended features. Weak emission near 40.4 km s^-1 sometimes appeared and usually was blended with the red-shifted complex. Extreme blue-shifted emission at 33.8 km s^-1 was first detected in 1986 November. Values of $v_{\rm e}$ and $v_{\rm s}$ are given in Table 1. The shape of the 1667 MHz spectrum at blue-shifted velocities changed less than that at red-shifted velocities. Significant variations in the Stokes V spectrum was observed at 1667 MHz. The 1665 MHz emission covered the velocity range from 35 to 46 km s^-1. Emission was present over almost the entire velocity range. Strong changes in the relative strength of the features were observed within less than two month intervals. Changes in the 1665 MHz profile shape were more prominent than at 1667 MHz. The Stokes V profile had very complicated and variable structure. Observations of W Hya made at 1612 MHz around the OH mainline maxima from 1986 February to 1995 December revealed, in 1992 August, faint polarised emission at $v_{\rm LSR}=36$ km s^-1 with the peak fluxes of 0.09 and 0.12 Jy in LHC and RHC, respectively (Fig. 5). 1${\sigma}$ in both polarisations was 0.02 Jy. The velocity of this peak is very close to the velocities of most prominent features at both mainlines.

Figure 3: Selected spectra of the OH 1667 MHz maser emission from W Hya in a) Stokes I and b) Stokes V taken from 1986 January to 1995 November. The flux density scale is shown by the vertical bar. JD$_{\rm m}$ dates are given in parentheses.

Figure 4: Same as Fig. 3, but for the OH 1665 MHz maser emission.

Figure 5: Spectrum in the 1612 MHz maser line from W Hya discovered around the OH mainline maximum of August 23-26, 1990. The spectrum presented is the average of 3 hours of observation. Thick and thin lines represent RHC and LHC polarisations respectively.

3.1.3 RT Vir

Figures 6 and 7 show selected OH maser profiles of RT Vir. The 1667 MHz profile had two emission complexes over a velocity range of about 15 km s^-1. The blue-shifted complex contained three blended groups of maser features centred near 10.5, 11.3 and 14 km s^-1 which are sometimes clearly distinct. The red-shifted emission had a velocity extent of 2 km s^-1. The 1665 MHz profile strongly deviated from the standard double-peaked profile. Sometimes faint emission appeared at the central velocity of 17.5 km s^-1 or the blue-shifted emission sharply dropped. The 1665 MHz emission was strongly circularly polarised and more variable than at 1667 MHz. The expansion velocity deduced from the 1665 MHz profile was about 0.5 km s^-1 lower than that deduced at 1667 MHz (Table 1).

Figure 6: Selected spectra of the OH 1667 MHz maser emission from RT Vir in a) Stokes I and b) Stokes V taken from 1982 April to 1995 November. The flux density scale is shown by the vertical bar. JD$_{\rm m}$ dates are given in parentheses.

Figure 7: Same as Fig. 6, but for the OH 1665 MHz maser emission.

3.2 Average profiles and variability index

The average OH maser profiles for the studied sources are shown in Figs. 8-10. The variability of maser emission for each spectral channel is estimated from the observed variability index  $\sigma_{\rm obs}$:

$$\sigma_{\rm obs}={1\over n}\sum\limits_{i=1}^n \vert S_i-S\vert,$$ (1)

where n is the number of observations, S_i is the flux density at the ith epoch, and S is the mean flux density. The variability index ${\sigma}$ (a lower limit to the intrinsic variability index) is then given by $\sigma=\sqrt{\sigma^2_{\rm obs}-\epsilon^2}$, where $\epsilon^2$ is the mean square error in flux densities. The profile asymmetry is defined as ( $S_{\rm pB}/S_{\rm pR}$)$\times$100%, where  $S_{\rm pB}$ and  $S_{\rm pR}$ are the peak flux densities at blue- and red-shifted velocities, respectively.

3.2.1 R Crt

The average maser profiles of R Crt at both transitions were strongly asymmetric; 91% and 84% in peak densities for 1665 and 1667 MHz lines respectively. Both emissions occurred within the same velocity range implying common envelopes (Szymczak et al. 1999). The variability indices generally followed the profile shapes, that is, when S is high then ${\sigma}$ is large, which would be expected for a linear amplification of maser emission in a homogeneous envelope.

3.2.2 W Hya

The average 1665 and 1667 MHz profiles of W Hya also showed significant asymmetry of 65% and 85% respectively. The 1667 MHz emission overshoots the 1665 MHz emission by about 1.5 km s^-1 which can be easily explained by the observational fact that the masers come from different regions (Szymczak et al. 1998). Broad and weak emission near the systemic velocity was present at both frequencies. This suggests tangential amplification in the envelope. The variability index across the profiles generally was proportional to the maser fluxes. At 1667 MHz, however, this index is slightly higher for the red-shifted emission than for the blue-shifted emission of similar average flux density. Considerable increase of ${\sigma}$ at a velocity of about 46.5 km s^-1suggests that at some epochs this feature was very weak or completely disappeared. Indeed, inspection of Fig. 3a revealed that this emission was present in two intervals; 1992 January - October and 1994 September - 1995 November. Further analysis in Sect. 3.4 shows that it significantly contributes to the integrated flux density. We conclude that at least the extreme red-shifted emission at 1667 MHz experienced eruptive variability.

3.2.3 RT Vir

The average maser profiles of RT Vir were asymmetric (70-50%) and of very different shapes in both transitions. The variability index across the 1667 MHz profile showed very unusual behaviour. There were three features near 10, 11 and 23.8 km s^-1 which disappeared at some epochs then reappeared at other ones. The features at 10 and 11 km s^-1 were observed from 1984 May to 1990 September, while the feature at 23.8 km s^-1 was seen only from 1988 November to 1989 April (Fig. A3). Analysis done below (Sect. 3.4, Fig. 14) clearly indicates that the bursts of emission near 10 and 11 km s^-1 largely contribute to the integrated flux density. Similarly the appearance of a feature centred at 23.8 km s^-1 resulted in an OH maximum of the red-shifted integrated emission. We note, that other OH maxima were not related to the bursts of individual features. The velocity extent of both maser lines of RT Vir indicates that they arise from a common envelope. Weak 1665 MHz emission at velocities of erratic 1667 MHz features shows a quite regular variability.

Summarising, we notice that the 1665 and 1667 MHz OH maser profiles of the studied semiregulars strongly deviate from the standard double-peaked profiles. It appears that changes in the 1667 MHz profiles due to bursts of individual features, tend to be more frequent than in the 1665 MHz profiles.

Figure 8: The average OH maser line profiles (thick lines and left axis) and the variability index across the profiles (thin lines and right ordinate axis) for R Crt.

Figure 9: Same as Fig. 8, but for W Hya.

Figure 10: Same as Fig. 8, but for RT Vir.

3.3 Flaring features

Maser features with eruptive variability were identified in RT Vir and W Hya. Variations of the linewidth at half maximum $\Delta V$ and peak flux density $S_{\rm p}$ of most interesting features at 1667 MHz during selected outbursts are plotted in Fig. 11. From 1985 May to 1987 July ( $1374\le {\rm JD}_{\rm m}\le 2031$) the feature centred at 8.8 km s^-1 from RT Vir underwent peculiar changes; $S_{\rm p}$ decrease was associated with $\Delta V$ re-broadening at $1462\le {\rm JD}_{\rm m}\le 1551$ (circles in Fig. 11a), while in the interval $1604\le {\rm JD}_{\rm m}\le 1817~S_{\rm p}$ rise was associated with $\Delta V$ narrowing (squares in Fig. 11a). Although the presence of each effect relied on four points spanning 89 and 213 days, we believe that these were real. In the same source a re-broadening of the feature centred at 10 km s^-1 was seen at $1574\le {\rm JD}_{\rm m}\le 1667$ (circles in Fig. 11b). It is worth noticing that variations of $S_{\rm p}$ of both features were uncorrelated before ${\rm JD}_{\rm m}=1817$. Furthermore, narrowing of the feature of W Hya centred at 46.5 km s^-1 was visible at $4899\le {\rm JD}_{\rm m}\le 4935$ (squares in Fig. 11c).

We found an inverse relationship between the linewidths and peak flux densities which followed a power law $\Delta V \sim S_{\rm p}^{-\alpha}$ with $0.19 <\alpha< 0.57$. Two possibilities can be considered to explain this effect. The line narrowing and re-broadening may result from blending of spectral features which are close in velocity. A blending effect possibly occurs for OH masers from W Hya where the red-shifted emission is composed of several spectral features. Interferometric observations (Szymczak et al. 1998) support this supposition. However, the OH maser spectra of RT Vir are much simpler than those of W Hya and the effect of blending is probably too weak to mimic the line narrowing and re-broadening. The second possibility is that variations of the linewidth against peak flux are intrinsic to the OH emission. Such power law variations with $\alpha=0.5$ are expected for unsaturated masers (Goldreich & Kwan 1974). Different values of $\alpha$ inferred for RT Vir possibly reflect a maser gain which changed in time from one maser feature to another. Uncorrelated variations of the peak fluxes in two spectral features of RT Vir strongly support this possibility. We conclude that bursts of OH emission from RT Vir with rise and/or decay times observed to be 90-200 days come from regions of different unsaturated maser gains.

Figure 11: Variations of the peak flux density (upper panels) and linewidth (lower panels) for the 1667 MHz features of RT Vir at 8.8 km s-1 a) and 10 km s-1 b), and of W Hya at 46.5 km s-1 c). Circles and squares denote the observing intervals of line re-broadening and narrowing respectively.

3.4 OH variation curves

Figure 12: Variability curves of R Crt. Optical data from AFOEV and VSOLJ a), the integrated flux densities (Stokes parameter I) at 1667 MHz (filled circles) and 1665 MHz (open circles) for the blue-shifted b), central c) and red-shifted d) emissions.

Figure 12 shows the integrated total fluxes ( $S_{\rm int}$) from R Crt at 1667 and 1665 MHz for the red-shifted, central and blue-shifted complexes. OH maser behaviour was similar at both frequencies. However, there was a general trend that the integrated flux of the blue-shifted emission was high when that of the red-shifted emission was weak. The behaviour of the OH emission at central velocities (7-16 km s^-1) was roughly similar to that at blue-shifted velocities. OH variability curves of R Crt presented high amplitude rises and declines of about 600-1200$^{\rm d}$ duration superimposed with shorter 550-610$^{\rm d}$ cyclic variations of smaller amplitude. During these last three cycles since 1990 September to 1995 November, when the radio data were better sampled, a modulation of the integrated flux density with periods of about 160-200$^{\rm d}$ was apparent. Optical data available from AAVSO AFOEV and VSOLJ were rudimentary, so that a detailed comparison with our data is not warranted. However, the optical brightness of R Crt may have been lower during the two last years of our OH observations (Fig. 12a). Furthermore, the weak 160-200$^{\rm d}$ modulations seen in the OH integrated flux density can correspond to the optical period of 160$^{\rm d}$ reported by Kholopov et al. (1985). We have used the most sampled parts of the OH variability curves (i.e., since 1990 September) for period analysis with the periodogram technique (Lomb 1976; Scargle 1982). With that technique, we found the two periodicities detected visually in the OH maser emission of R Crt (i.e., $560\pm 15^{\rm d}$ and $227\pm 8^{\rm d}$, Table 2). The non-sinusoidal shape of the variability curves and large changes in amplitude from one cycle to other are probably the reason why the probability of a 160$^{\rm d}$ period was below 95%.

Figure 13: Same as in Fig. 12, but for W Hya. Variations of the integrated flux densities of the extreme blue-shifted emission near 33.8 km s-1 e) are shown.

The integrated OH maser fluxes of W Hya showed considerable variations, sometimes by about an order of magnitude during less than 600$^{\rm d}$, in both mainlines (Fig. 13). The behaviour of the blue-shifted and red-shifted emissions was roughly similar in both lines over the whole interval of observations. The 1667 MHz emission at central velocities generally followed the changes of the red-shifted emission but with more moderate amplitude. The variations of the central velocity emission at 1665 MHz were small. Good sampling of data from 1993 November to 1995 December allowed us to identify two consecutive maxima of small and large amplitudes with a period of 380$^{\rm d}$. Furthermore, secondary maxima were seen in the 1667 MHz red-shifted emission, while at 1665 MHz shorter variations with a period of about 200$^{\rm d}$ were evident. The periodogram analysis of these observations revealed periodicities of $362~\pm~7^{\rm d}$ at both OH maser frequencies (Table 2). The main OH period of 362$^{\rm d}$ agrees very well with the average, optical period (Kholopov et al. 1985). On the average the OH maxima were delayed by $16\pm 10^{\rm d}$ with respect to the optical maxima deduced from VSOLJ and AFOEV data. The phase lag (i.e., the time shift) between the OH 1667 MHz flux curves in the red-shifted and blue-shifted emission was $20\pm 13^{\rm d}$. This corresponds a shell of radius 9.0- $42.6\times 10^{15}$ cm. We note that this lower limit was a factor of two higher than the average radius measured with MERLIN (Szymczak et al. 1998). This suggests that in the case of W Hya the lower limits of the phase lag measurements should be considered as roughly consistent with the interferometric data. We observed a delay of $64\pm 14^{\rm d}$ between the OH 1667 MHz flux density maxima of the extremely blue-shifted peak at 33.8 km s^-1 and the standard blue-shifted peak at 36 km s^-1. This implies that the extreme blue-shifted emission, unresolved with MERLIN (Szymczak et al. 1998), arises at a distance of about $2.9\times 10^{16}$ cm from the central star (see Sect 4.1).

   

Table 2: Variability periods of the studied semiregulars.

Star	Optical period1 (days)	OH periods (days)
R Crt	160	$227\pm 8$; $560\pm 15$
W Hya	360	$362\pm 7$
RT Vir	155	$112\pm 11$; $170 \pm 7$

¹ From Kholopov et al. (1985).

Figure 14: Same as in Fig. 12, but for RT Vir.

The OH variability curves of RT Vir are shown in Fig. 14. The variations of the red-shifted and blue-shifted parts of the spectra in both OH mainline were generally independent. Rises and decays of the OH flux by a factor of 3-6 during 120-140 days and low amplitude changes lasting a few thousand days were observed. Weak 1665 MHz emission close to the stellar velocity was sporadically present. Over the best sampled part of the integrated flux curves (1993 November-1995 November) we found a $170\pm 7^{\rm d}$ periodicity in the 1667 MHz red-shifted emission. Furthermore, a shorter cycle of $112\pm 11^{\rm d}$ duration was observed in both mainlines. Their formal confidence limits were above 0.95. Those OH periods differ by 15-43$^{\rm d}$ from the optical period of 155$^{\rm d}$ quoted by Kholopov et al. (1985). The optical data from the interval of our observations are too incomplete to look for any relation with the radio variations.

 

 

Table 3: Amplitudes ($\Delta m$) of OH variations between consecutive minima and maxima in the three semiregulars. In parentheses are given the amplitudes over the entire intervals of observations.

Source	1665 MHz		1667 MHz
	blue	red	blue	red
R Crt	0.92-2.45  (5.3)	0.81-1.85  (4.7)	1.05-2.41  (6.2)	1.01-1.41  (2.0)
W Hya	0.34-2.44  (5.0)	0.92-3.97  (3.8)	0.60-3.68  (3.8)	0.52-1.68  (3.1)
RT Vir	0.42-2.42  (3.9)	0.75-2.30  (2.7)	0.57-0.71  (2.9)	0.34-2.08  (2.1)

In order to quantify better the OH variability curves we measured the amplitude between a consecutive maximum and minimum of the total integrated flux densities defined as $\Delta m=2.5\log(S_{\rm int}({\rm max})/S_{\rm int}({\rm min}))$. The ranges of amplitudes measured in both mainlines for the blue-shifted and red-shifted emissions of the 3 semiregular stars are given in Table 3. We note that the ranges of OH amplitudes of the studied semiregulars (0.3-4.0) are similar to that observed for Miras (Etoka & Le Squeren 2000). Amplitudes of  $S_{\rm int}$, also measured in magnitudes, over the entire intervals of observations, given in parentheses in Table 3, range from 2.0 to 6.2 which are comparable to those values reported for some Miras (Etoka & Le Squeren 2000). In all three stars these amplitudes are higher for blue-shifted emission than for red-shifted emission for both mainlines. In general, $\Delta m$ is higher at 1665 MHz than at 1667 MHz. This suggests, at least for W Hya, that the variability decreases with the radial distance of the maser envelope from the star.

3.5 Line ratio

Figure 15: Ratio of the integrated flux density at 1667 MHz over that at 1665 MHz (filled symbols) and the integrated flux density summed over both mainline transitions (open symbols) as a function of time for the three semiregular variables. For each source the blue- and red-shifted emission is shown separately in upper and lower panels, respectively.

The ratios of the integrated flux density at 1667 MHz to that at 1665 MHz for both the blue-shifted and red-shifted emission for the 3 sources are presented Fig. 15. For the blue-shifted emission of R Crt, this ratio was about 2 during most observing epochs. At $3400<{\rm JD}_{\rm m}<3800$ only this ratio was as high as 6-10. This ratio for the red-shifted emission of R Crt was about 2 at the following JD$_{\rm m}$ intervals: 0-400, 3200-4200 and 4350-4440, while during other epochs it varied from 4 to 14. In W Hya and RT Vir the ratio was generally about 2 for the blue-shifted emission and rarely higher than 4. In turn, for the red-shifted emission of either source the ratio was typically above 4 and could exceed 20. In all three sources we found a trend for the ratio to be about 2 during epochs of high OH activity, reaching its highest values during periods of low level maser emission. The line ratio value is suggested to be a function of the fractional abundance of OH molecule (Collison & Nedoluha 1994); an envelope of lower fractional abundance has dominant 1667 MHz emission. It is likely that during a period of quiet OH emission the fractional abundance of OH decreases and 1667 MHz emission becomes dominant. Our results seem to support the suggestion of Collison & Nedoluha.