Astron. Astrophys. 334, 1016-1027 (1998)

4. Results

4.1. General characteristics of the emission at 183 GHz

Figs. 2a-c show the observed spectra in the various objects. The dotted line in each panel indicates the stellar velocity, which has been calculated from our CO spectral observations or taken from the literature. Table 3 lists the line parameters which are related to the observations at 183 GHz.

Table 3. Line parameters of the 183 GHz line observations. We list the LSR velocity of the star (), the maximum value of with the rms noise of the spectrum (1 ) in parenthesis, the velocity-integrated intensity (W), the full power line width (, units of km s^-1) and the LSR velocity of the peak emission (, units of km s^-1).

Examination of the spectra reveals that the emission at 183 GHz is of maser nature in most of the objects. The line profiles at 183 GHz usually consist of one or more narrow spectral features superimposed on a broader component. The narrow components do not have any counterpart in the CO emission, which would be thermalized in the region where the emission at 183 GHz originates. Since the intensities at 183 GHz are generally 3-30 times higher than those of CO and the opacity of the CO line is at least moderate, the emission at 183 GHz must be subjected to maser amplification. The calculations of statistical equilibrium populations which will be discussed in González-Alfonso & Cernicharo (1998; see also Neufeld & Melnick, 1991) show that the inversion of the transition at 183 GHz takes place under a variety of interesting physical conditions.

The line profiles at 183 GHz are different in shape from object to object. In stars such as V Cam, R LMi, R Leo, R Aql, T Cep, µ Cep, and R Cas, the line at 183 GHz peaks at a velocity () very close to the stellar velocity (), thus suggesting that the bulk of the emission originates in the immediate neighborhood of the star and/or that the greatest maser amplification occurs in the tangential direction (i.e., perpendicular to the radial direction). In these objects the velocity at which the emission at 183 GHz is maximum approximately coincides with that at which the bulk of the SiO emission originates. In addition to one component at approximately the velocity of the star, some of these objects show emission at other velocities shaped as line wings or "plateau emission" (V Cam, R Leo, R Cas) and/or as a second velocity component (V Cam, R Aql, R Cas). The 183 GHz line width is considerably narrower than the CO The objects which possess these characteristics have values lower than 2 y^-1 (see Table 2) and constitute Group I objects.

In the stars IRC+10011, S Per, NML Tau, IRC+60154, GX Mon, RT Vir, RX Boo, VX Sgr, OH63.3-10.2, NML Cyg and OH 104, the peak emission is shifted towards velocities close to the terminal velocity () of the envelope, as it can be verified when comparing the line profiles at 183 GHz with those of CO These objects are placed together to constitute Group III objects. The stars from Group III show two emission peaks, one red-shifted and the other blue-shifted relative to . The two peaks are distributed almost symmetrically relative to . In most of these stars (all but NML Tau, OH63.3-10.2 and OH104.9+2.4) the blue-shifted peak is at least as intense, if not more, than the red-shifted one. Furthermore, some objects show emission at intermediate velocities (around ) in form of plateau emission. These properties characterize also the OH maser lines, and indicate that the emission at 183 GHz originates in regions distant enough from the star as to allow the gas to reach velocities close to . Except for RT Vir and RX Boo, the stars belonging to Group III have higher than 10^-6 y^-1 ; in general, these are the stars with the highest (Table 2).

The emission at 183 GHz in the rest of stars present characteristics common to the former groups, and they constitute Group II. It consists of stars Y Cas, W Hya, S Crb and U Her. These stars have the emission peak slightly blue-shifted relative to , and show a wider spectral component resembling plateau or emission wings at velocities around . Nevertheless, the emission peak has a velocity which is far from being , and the line profile at 183 GHz does not show a red-shifted peak relative to . The mass loss rates in these objects are similar to those from Group I.

4.2. Comparison of the emission at 183 GHz with the emission of the other lines of water vapour

The p-H₂ O line at 325 GHz was observed in eight objects of the sample. Three of them, RT Vir, RX Boo and NML Cyg, are classified as belonging to Group III. The line profile at 325 GHz in RT Vir and NML Cyg consists of a blue-shifted peak relative to and an emission plateau, differing from the line profile at 183 GHz in the velocity of the emission peak relative to , , which is lower than that at 183 GHz, . Another difference between the two lines is that the line profile at 325 GHz does not show a red-shifted emission peak relative to . The less pronounced shift of the maximum at 325 GHz is an indication that this line forms in more internal regions than the line at 183 GHz. This is a natural consequence of the higher excitation energy of the levels involved in the 325 GHz line. RX Boo shows very weak emission at the velocity of the blue-shifted peak observed at 183 GHz. The profile at 325 GHz in other stars, with lower than the former, differs appreciably from the profile at 183 GHz, with the emission peak at 325 GHz systematically red-shifted relative to that at 183 GHz and also relative to . The bulk of the emission in both lines originates in different regions, thus indicating that the optimal physical conditions for the inversion and amplification are different for these transitions. The width of the line at 325 GHz, (325), is narrower than that at 183 GHz, (183).

The profiles of the o-H₂ O line at 22 GHz also differ from the line profiles at 183 GHz in objects belonging to Groups I and II. In R Leo and T Cep, where the intensity at 183 GHz is relatively high, the line at 22 GHz was not detected. In those sources where the velocity of the emission's maximum at 183 GHz is appreciably separated from , the velocity of the emission peak at 22 GHz does not coincide with the former, and takes on values closer to . Generally, the emission at 22 GHz is dominated by a narrow spectral component at approximately the same velocity as that of the star (V Cam, R LMi, W Hya, S Crb, R Aql, R Cas), with a contribution of a second component (W Hya) or of wing-like and/or plateau-like emission with much lower intensity than that of the emission peak (R LMi, W Hya, R Aql, R Cas). In the objects from Group III, which usually have larger values of , the spectral emission at 22 GHz resembles the emission at 183 GHz in the following way: the emission peak is blue-shifted relative to (IRC+60154, RT Vir, NML Cyg, OH104.9+2.4), and it is observed an emission plateau at velocities closer to , even though its intensity, relative to that of the emission maximum, is much weaker than that at 183 GHz. The SiO spectral emission is usually quite different from that at 183 GHz, except in the objects with low where the velocity of the emission maximum in both lines is similar to .

4.3. Time variations of the emission at 183 GHz

Fig. 5 shows the spectra at 183 GHz observed towards some sources in several periods of observation. Among the sources observed in different periods, there are objects from Group I (R LMi, R Leo, R Aql, R Cas), Group II (W Hya, U Her) and Group III (RT Vir, RX Boo, VX Sgr, NML Cyg). Column labeled F₅ in Table 1 indicates the panels of Fig. 5 which display the observations of these sources achieved in various epochs.

Fig. 5. a upper left, b upper right, c middle left, d middle right, e lower left. Spectra at 183 GHz observed towards various stars in different epochs. The dashed lines in each panel indicate the stellar velocity. The panel corresponding to a given source is indicated in Table 1 (F5)

Except for the differences in the scale of intensity, which are probably due to errors in calibration, most of the objects show essentially the same line profile throughout various observational periods. The most pronounced variations in the line profile are observed in R Cas and R Aql (objects from Group I), and in U Her (object from Group II). In R Cas, the 1991 spectrum shows that the emission peak lies on the part of the profile which is blue-shifted relative to (the phase of the star was then ), while in 1994 () the peak emission lies on the red-shifted part of the spectrum. In R Aql the variation is less pronounced, but the maximum of intensity observed in 1991 () is slightly blue-shifted relative to 1994 ( ; the velocity of the second peak in the blue remains unvariable). The line profiles observed in U Her in 1989 and 1991 ( plus respectively) are similar, and show two peaks shifted toward the blue relative to . In 1994 () the profile showed a single peak at intermediate velocities of the two observed in the preceding periods. The emission in the wings is similar in the three mentioned periods. In W Hya (Group II) it seems also that there is some shift in the velocity of the peak emission, but the line profile is similar in 1989 and 1991.

The objects from Group III show less variations in the line profile than the objects from Groups I and II. The spectral appearance of the emission in VX Sgr and NML Cyg in 1991 and 1994 is essentially identical. Among all stars which have been observed during different periods, the latter have the largest . In RX Boo the main difference observed among the profiles compiled in distinct epochs is the disappearance in 1994 of a spectral component at the velocity of the star; this component is observed in the 1989 and 1991 spectra. The width and intensity of the emission peak relative to the plateau was also accompanied by a variation of a factor between 1991 and the other two periods. In RT Vir the intensity ratio of the blue-shifted component to the red-shifted one varies between 1989 and 1994 by a factor of . RT Vir and RX Boo are within Group III the stars with the smallest .

In general terms, the major differences in the spectral emission at 183 GHz among different periods are observed in the objects from Groups I and II, where the emission originates at velocities close to . The main variation found in RX Boo (Group III) is observed in the emission at the velocity of the star. An exception to this rule is the case of RT Vir commented above.

In objects where the spectral emission does not change shape during different periods, the intensity variations are very likely due to the errors in the calibration of the observations. Differences in intensity are lower than a factor 2.5 between 1989 and 1994, which is compatible with calibration uncertainties. Between 1991 and 1994, the difference in the intensity scale of VX Sgr is compounded by a factor , which is still compatible considering the calibration uncertainties in both periods. Since the calibration of the 1994 data seems more accurate than that of the 1991 period, we will refer henceforth, and whenever possible, to the observations conducted in 1994.

4.4. Correlation between the line width at 183 GHz and

As stated before, the line profile at 183 GHz of the objects from Group III presents spectral features close to . These objects have values higher than the objects from other groups. Thus, we could deduce a global trend consisting of the velocity shift (relative to ) of the emission peak that increases with . This trend is shown in Fig. 6, which plots versus for the various objects. In all stars, except for R Cas and T Cep, corresponds to the emission peak in the part of the spectrum that is blue-shifted relative to (including the cases where the absolute maximum of emission is red-shifted, such as NML Tau, OH63.3-10.2 and OH104.9+2.4). NML Tau shows three peaks of similar intensity in the blue; in this case we have chosen for the average velocity of the three peaks. V Cam and R Aql show the emission peak at the velocity of the star, but also a second component blue-shifted relative to . We have chosen for the velocity of this second component. The uncertainties affecting come mainly from when is low, i.e., for objects with a low value of . A typical uncertainty of 1 km s^-1 in gives rise to an uncertainty of 0.1 in for an object with km s^-1. Since the uncertainty in is high, the results in Fig. 6 have to be considered as indicative of a global tendency. This global trend is described by the straight line fitted onto the data (however, note that the fit of a straight line is not physically justified, since, for instance, the best fitting curve would tend asymptotically to 1 as increases). For this fit we obtain and .

Fig. 6. The velocity shift of the emission peak ( - ) relative to the terminal velocity of the envelope () versus the logarithm of the mass loss rate. The fitted line has a dispersion of and the correlation coefficient is

Some simple arguments account for the above correlation between and : as increases, the line is appreciably inverted at larger radial distances, where because of the fact that the logarithmic velocity gradient () decreases, the radiation focuses strongly on the radial direction producing the emission peaks in the line profile at velocities close to . On the other hand, we have already noted that the blue-shifted spike is in most stars more intense than the red-shifted one. This observation can be explained upon the amplification of the stellar emission by the gas approaching the observer (González-Alfonso & Cernicharo, 1998).

Fig. 7 plots the full width of the line at 183 GHz, , divided by 2 , versus . The value of has been calculated from the difference in velocity of the two extreme channels which have an intensity ( is the rms noise of the spectrum) from which one channel width has been subtracted. In this manner, has an uncertainty which depends on the spectral noise and on the velocity resolution of the spectrum. The velocity resolution in the spectra of the weakest sources was degraded in order to obtain a reasonable signal to noise ratio; for these sources, the uncertainty in is 1-3 km s^-1, and the uncertainty in is 0.1-0.2. It is also worth mentioning that the sample favours, in relation to the values of , the objects closest to the Earth (which are also the ones with the lowest ): is determined in many cases by the emission shaped as wings or plateau. It is an emission that would not have been detected with the same spectral noise if the object were located much farther from the observer. Since the nearest objects have also the lowest , this effect will tend to partially camouflage the correlation between both variables. Nevertheless, Fig. 7 shows a correlation between them (), and the slope of the fitted straight line is essentially the same as in Fig. 6.

Fig. 7. The full width of the line at 183 GHz relative to twice the terminal velocity of the envelope () versus the logarithm of the mass loss rate. The fitted line has a dispersion of and the correlation coefficient is

Figs. 6 and 7 allow to establish a more quantitative difference among the sources belonging to distinctive groups. The emission at 183 GHz in the stars from Group III is characterized by and (except S Per). The stars from Group II have and and the Group I stars have and .

4.5. Correlation between the luminosity at 183 GHz and

Fig. 8 shows a logarithmic plot of the peak intensity () at 183 GHz multiplied by (which we will call hereafter ) versus . represents, therefore, the maximum value of which would be obtained if all the sources were located at a distance of 1 pc from the Earth. A straight line has been fitted onto the data. The dispersion of the least-square fitting of a straight line and the correlation coefficient for versus are and , respectively.

Fig. 8. Logarithmic plot of the peak intensity at 183 GHz corrected for the distance versus the mass loss rate. The fitted line has a dispersion of and the correlation coefficient is . The segments intersecting the data points indicate the paths that the points would travel if and were both underestimated or overestimated by at most a factor of 3

It is important to evaluate whether the correlation between and could be an artifact of the errors in and . In Fig. 8, the segments intersecting the data points indicate the paths that the points would travel if and were both underestimated or overestimated by at most a factor of 3. As it was mentioned above, if all the values of and were underestimated or overestimated by a similar factor, the correlation would remain the same. However, Fig. 8 shows that the correlation between and may be seriously distorted if the (and hence ) values of the objects with the lowest are systematically underestimated, whilst the (and hence ) values of the objects with the highest are systematically overestimated. Since this possibility cannot be disregarded, the correlation between and , although probably real, must be considered with some caution.

Fig. 9 shows a logarithmic plot of the velocity-integrated intensity W of the emission at 183 GHz multiplied by (hereafter ) versus . represents the integrated intensity one would expect in case all the sources were located at a distance of 1 pc from Earth. A straight line has been fitted onto the data. The fit dispersion and the correlation coefficient are and , respectively. According to the figure, the slope of the fitted line is . Similarly to Fig. 8, the segments intersecting the data points in Fig. 9 indicate the paths that the points would travel if and were both underestimated or overestimated by at most a factor of 3.

Fig. 9. Logarithmic plot of the velocity-integrated intensity at 183 GHz corrected for the distance versus the mass loss rate. The fitted line has a dispersion of and the correlation coefficient is . The segments intersecting the data points indicate the paths that the points would travel if and were both underestimated or overestimated by at most a factor of 3

In Fig. 9, the slope of the fitted line differs appreciably from the one fitted on versus , whereas the correlation coefficient also increases considerably. The fit of the data points is quite unsensitive to the individual errors in (and hence in ): these errors are likely to shift the points in parallel to the fitted line. The correlation between and would remain if the errors for and do not amount for much more than an estimated factor of 3. The values of are also quite impervious to spectral noise, and the average quadratic deviation is similar to the uncertainty in the absolute calibration of the observations. Hence, Fig. 9 indicates that the integrated intensity of the p-H₂ O emission at 183 GHz is proportional to the mass loss rate of the star within a range of values for that exceeds three orders of magnitude. This relation is compatible with the possibility that the bulk of the maser emission is saturated in the various CEs and the water vapour abundance does not vary significantly among the stars of our sample.

The slope for the fit of versus depends only in small measure on the considered subset of objects: a fit for the sources belonging exclusively to Group III yields a slope for versus of (). It is in accordance with the notion of saturated emission, as it will be shown in González-Alfonso & Cernicharo (1998).

© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

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