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Astron. Astrophys. 351, 644-656 (1999)

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4. Discussion

4.1. Velocity variations

The short period SRVs fit well into the picture indicated by the variables with longer periods. Typical amplitudes for these stars are found to be about 2 to 4 km s-1. In most cases the two wavelength regions investigated agree in their amplitude and shape of the variations. Some stars seem to vary with the period of the visual brightness variations, others behave irregularly or may follow a different period. Obviously, variations do not always follow the same period for every cycle making a merging of observations from different cycles almost impossible. Representative for this behavior are the variations observed in g Her or TU CVn.

The third type of variability found within the small sample observed is visible in TT Dra, TX Dra and BQ Gem. OP Her and RV Boo might be further candidates for this type, but the uncertainty in period actually does not allow a definite conclusion. Both objects show variations that might indicate a period somewhat smaller than the GCVS4 period. The variations in these stars look very similar to the variations found for RU Cyg, but both their amplitudes and periods are a bit smaller. It cannot be excluded that such variations could be found also in other stars, but they are masked by bad phase coverage or uncertainties in the period. As mentioned above, TT Dra might even behave similar to the miras but with a much smaller velocity amplitude.

Furthermore, two stars of our sample, RR CrB and X Her, show variations that might be connected both to short period and long period variations. For both stars a secondary period is indicated from the light curve. In two more objects, g Her and RY CrB, such a "double variation" in the radial velocity data may be visible as well. This result implies that the secondary, longer periods could be very important for the understanding of the short period semiregular variables. However, for RY CrB the variations might be due to orbital motion around a companion star.

4.2. Absolute velocities

The observed difference between center of mass velocities and velocities derived from the CO [FORMULA]v=3 lines might be due to one or more of the following reasons:

4.2.1. Technical reasons

  • The same explanation is valid that was found possible for g Her, i.e. wavelength region 1 would generally underestimate the velocity amplitude. In fact, inspection of the velocity curves of both regions shows that this might be true for several objects. However, it is not found in all stars and the difference in amplitude beween the two wavelength regions is not in all cases large enough to explain the observed discrepancy in general.

  • The assumption is wrong that the velocity of g Her is almost constant between the two nights: Fortunately, FTS spectra of two more stars have been obtained in that night (see Table 2). The velocity difference between the calculated Coudé Feed value and the FTS value for RR UMi is 0.1 km s-1 and for X Her 0.4 km s-1. Both differences are almost within the uncertainties of the FTS/Coudé-Feed velocities, but even if the difference would indicate an error in the FTS velocity of g Her, it is too small to shift the detected asymmetry sufficiently.

  • One aspect that cannot be excluded as it has not been tested up to now is that a velocity difference occurs between the 2.2 µm region (FTS-spectra) and the 1.6 µm region (Coudé-Feed). Such an assumption is not supported by the results from miras where the velocities from the high excitation CO 1st overtone lines in the K-band and the CO 2nd overtone lines show the same velocity behavior 2. However, the possibility exists that semiregular variables behave differently. If so, one can think of two possibilities: Either the velocity variation at 2.2 µm is shifted in phase relative to the variation at 1.6 µm, so that a velocity difference occurs. Or the velocity amplitude at 2.2 µm is significantly larger than at 1.6 µm. The disadvantage of both explanations is the fact that such a behavior is not observed in miras. These are thought to be even more extended than SRVs, and a main condition to achieve such a difference will be a very large extension of the object. Tuthill et al. (1998) find that for W Hya, a semiregular variable, radii at 1.65 and 2.26 µ are very similar (see Hinkle et al. 1997for the velocity curve of W Hya). Furthermore, typical indicators of shock fronts (emission lines, line doubling), that would allow a large velocity difference on a small scale, were not found in the SRVs of our sample. Although this explanation cannot be ruled out without a detailed modelling of AGB-star atmospheres, it seems rather unlikely.

4.2.2. Literature values

  • The literature values are inaccurate: This would be quite probable in some cases as already mentioned in the previous section. Still, incorrect values should not be systematically biased towards larger velocities. Furthermore, obvious cases of wrong velocities in the literature have been corrected by our own `blue' spectra.

  • The literature values are correct but do not represent the center of mass velocity: Most of the literature data (and also our own data indicated by LZ in Table 3) are based on visual/photographic spectra. From different investigations (e.g. Hinkle & Barnes 1979) it is known that for miras the velocity derived from blue atomic lines is not identical with the center of mass velocity, but is red-shifted. In our case the literature values are also red-shifted relative to the velocities derived from the CO lines. On the other hand, system velocities derived from radio CO lines, which exist for a small part of the sample, have been used in the list of literature data in Table 3. They exhibit the same direction of the velocity shift as the `blue' velocities. But it has to be noted that the velocities from radio CO lines, although in principle very accurate indicators of the center of mass velocity, display a significant scatter of up to a few km s-1 within the literature. Furthermore, radio CO line profiles were found to be asymmetric in some cases. In these cases deriving a center of mass velocity from these lines becomes quite difficult.

4.2.3. Additional velocity components

As the above listed attempts could not or at least not completely explain the observed difference, it has to be assumed that we see outflowing matter over most of the cycle. It is quite unlikely that no inward movement of material happens.

  • The long period option: It might also be the case that we do not see these objects at their center of mass velocity because we did not observe long enough. Secondary periods of SRVs appeared already several times in this paper. If they are of the order of 1000 days, our sampling might be not sufficient. This interpretation was already suggested for W Cyg (Hinkle et al. 1997). On the other hand, such a long `main' period of pulsation, that is not or only marginally expressed in the light changes, seems quite unlikely. Such a long time variation could also be due to unknown companions. However, this is indicated only for a few stars of our sample. Furthermore it does not allow to explain a systematic difference between the observed velocity and the literature value, for one would expect a scatter around the center of mass velocity in that case.

  • Temperature effect: Maybe we see only one component because of the difference in temperature between the hot outflowing material and the cool infalling matter, so that the latter might not be visible. This would be in agreement with the fact that line doubling is never observed in these stars. On the other hand, we have to note that the lines are visible throughout the whole light cycle. We found no spectrum where the lines actually vanished which would then correspond to a phase of `pure' infall.

  • Granulation: A temperature effect as described before could get important, if we see an overlap of pulsation and convection. A velocity asymmetry could originate from large convective cells at the surface that are thought to be present in these stars (Schwarzschild 1975, Weigelt et al. 1998). The phenomenon of an overall blue shift of the measured velocity by convection effects is well known from the sun, resulting from the interplay between granular intensity and velocity fields. The general case of granulation in stars has been discussed by Dravins (1987), but investigations on cool and extended objects are lacking. However, only model calculation could proove whether the size of the velocity shift can be explained in this way, which is beyond the scope of this paper. We just want to mention that the spectral features investigated in this paper are almost exclusively line blends or even molecular band heads. Therefore an analysis of the line profiles that would lead to information on the origin of the observed variations is not feasible. Compared with the other possibilities discussed convection seems to be a realistic possibility to explain the observed phenomenon. In this context it is interesting to note that two of the three irregular variables in Table 3, µ Gem and UW Lyn, clearly show the same direction of the velocity shift. Therefore to have a common explanation for all stars of our sample a mechanism that can be found in every cool and extended atmosphere, like convection, seems preferable.

Observational material presented in this paper as well as in the literature does neither exist for a sample sufficiently large nor is it accurate enough both in velocity and in the coverage of the whole light cycle to allow any final conclusions at the moment.

Different answers might be true for different objects. As this velocity difference was found for some long period SRVs (Hinkle et al. 1997), too, it might be a common feature for semiregular variables. In that case, however, a common explanation for all SRVs would be more likely.

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999