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

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3. Results

3.1. Velocity variations

The two wavelength regions were analyzed separately. Each region had a different reference point as observations of one night were done in only one wavelength range. Both reference points were set to a velocity equal to zero. This causes a velocity shift between the resulting velocity curves of the two regions, which depends on the variability of the object between the two reference points. However, in most cases the difference in velocity between the two reference points was found to be small compared to the total velocity variations. Still we note that for a large fraction of the stars in the sample wavelength region 2 gives slightly higher velocity values than region 1. It is most likely that an undetected small shift in the wavelength calibration of the reference night relative to the reference night of region 1 is responsible for this difference. As the velocity curves of both regions show a similar shape, it can be excluded that such a wavelength shift has any importance in the other observing nights. Visual phase information was available for some objects from parallel observations by the AAVSO or from later data obtained by the author with an automatic telescope (APT, the telescope and the observing program are described in Strassmeier et al. 1997 and Lebzelter 1999b, respectively, the results will be presented elsewhere). One well defined light maximum or minimum within the time spanned by our observations was determined and used to set the zero point of the phase. From this zero point the phases of all observations were calculated. However, SRVs can show significant cycle to cycle variations both in period lengths as well as in the shape of the light curve. This makes a continuous calculation of phases difficult. For this investigation the phases were calculated using the mean (GCVS4) period. Therefore it has to be kept in mind that due to this property of semiregular variations a calculated maximum phase does not have to be in agreement with an observed maximum. This has to be considered when discussing periodic and non periodic variations. Where no phase information was available the first observing night (JD 2449785) was taken as phase 0.

3.1.1. Individual velocity curves

The velocity variations will be discussed star by star starting with the objects with the shortest periods. The velocity curves can be found in Figs. 4 to 18. The typical uncertainties of the velocity measurements of each night are plotted as error bars. The phase coverage of the radial velocity measurements allows in some cases only the estimation of a lower limit to the amplitude. The period listed in each figure caption is the one from GCVS4 (also listed in Table 1).

o1 Ori (Fig. 4) is a double star with a white dwarf companion. Parameters describing the orbital motion are missing in the literature. The evolutionary status of this object was discussed in detail by Jorissen & Mayor (1992). In Fig. 4 we plotted the velocity shifts against Julian Date as on the one hand the period of the intrinsic variations is not well known (GCVS4), and on the other hand the observed variations might be dominated by the orbital motion. Variations in both wavelength ranges agree satisfactorily. The maximum velocity difference observed within anyone of the two ranges is approximately 4.5 km s-1. Brown et al. (1990) reported several velocity measurements at 7500 Å over a time span of 330 days. The maximum difference found from these velocities is 2.2 km s-1. The available data are not sufficient to derive the intrinsic velocity variation. A hand-drawn interpolation of the velocity curve suggests that we probably see a combination of orbital motion (or a secondary period) and variations on a short time scale, e.g. the GCVS4 period.

[FIGURE] Fig. 4. Velocity variations of o1 Ori (P[FORMULA]30d) versus time. Solid boxes denote measurements from wavelength region 1, while open circles mark data from wavelength region 2. Time is JD minus 2440000.

BC CMi shows only very small variations of about 1 km s-1 (Fig. 5). It is not clear whether these variations are related to the photometric period. Variations on a significantly longer time scale cannot be excluded, but are also not really supported by the data. Due to the very short period of the star, about 10 cycles (period = 35 days) lie between the 1995 and the 1996 observations. This makes a combination of the results quite difficult. After all, for that small velocity changes, the typical error of the velocities of about 350 m s-1 strongly limits the reliability of the results. The position of the star in the sky did not allow to observe this object in May and June 1995.

[FIGURE] Fig. 5. Velocity variations of BC CMi (P[FORMULA]35d). Same symbols as in Fig. 4.

RR UMi is the second double star of our sample. Its orbital elements are well known so that we used the orbital period to calculate the phase (Fig. 6). Our observations cover about half a cycle. In Fig. 6 we additionally plotted the expected velocity variation due to the orbital motion of RR UMi calculated from the parameters given by Batten & Fletcher (1986). For ease of comparison, the Coudé Feed velocities have been shifted to overlap with the (orbital) velocity curve from Batten & Fletcher. Note, that at this point we measured only velocity shifts . It can be seen that the variations we observe from the CO lines are mainly due to the orbital motion. This star has been observed two times in some nights. The variations found within one night are very small.

[FIGURE] Fig. 6. Velocity variations of RR UMi (P[FORMULA]43d). Same symbols as in Fig. 4. The double star period (748.9d) has been used to calculate the phase. Expected velocity variations due to orbital motion are marked with crosses (see text).

The light variations of TU CVn do not follow the mean period accurately. For phase estimation we used a maximum derived from our own light curve data at JD 2450420. The velocity variations are plotted in Fig. 7. Variations of about 3 km s-1 are indicated in both wavelength regions. Plotting all observations between phase 0 and 1 did not lead to useful results. The irregularities in period found from the visual light curves seem to be represented in the velocity variations, too. Phase estimation will therefore not be very reliable.

[FIGURE] Fig. 7. Velocity variations of TU CVn (P[FORMULA]50d). Same symbols as in Fig. 4.

Only a few data points were obtained for BQ Gem . The resulting velocity variations are plotted in Fig. 8. An estimate of the amplitude gives 1.5 km s-1. The lower panel of Fig. 8 gives the velocity variations versus phase. Periodic changes are possible.

[FIGURE] Fig. 8. Velocity variations of BQ Gem (P[FORMULA]50d). The lower panel shows the variations versus estimated phase. Same symbols as in Fig. 4.

No phase information was available for ER Vir (Fig. 9). For the observing runs in 1995 an untypically large shift in velocity is observed between the two wavelength regions. The origin of this is not clear. Reducing all data to one period (lower panel of Fig. 9) shows no expressed periodicity. The amplitude is estimated to be 2 to 2.5 km s-1. The scatter is quite large and as a comparison with the light curve was not possible, a definite description of a possible regularity cannot be given.

[FIGURE] Fig. 9. Velocity variations of ER Vir (P[FORMULA]55d). The lower panel shows the variations versus estimated phase. Same symbols as in Fig. 4.

Velocity variations found for RR CrB are plotted in Fig. 10. Plotting the data simply in time (bottom axis in Fig. 10) suggests variations with a period several times the period found in the GCVS4. A secondary period of 377 days has been found by Houk (1963) and the corresponding phases (relative to the first observation) can be seen in the top axis of Fig. 10. This period leads to a quite reasonable result. The long period case would lead to a velocity amplitude of the order of 3 to 3.5 km s-1. However, the velocity curve shows variability on a shorter timescale with a a smaller amplitude of about 1 km s-1, too. A combination of the GCVS4 (short) period option with the long period of Houk seems likely. The long period behavior might also be due to an orbital motion, but no indications exist that this object is a binary.

[FIGURE] Fig. 10. Velocity variations of RR CrB (P[FORMULA]61d). Same symbols as in Fig. 4. The bottom axis gives the cycles calculated with the GCVS4 (short) period. The top axis gives the phase calculated from the long period of 377d (see text).

The observed velocity changes of TX Dra suggest a possible periodic behavior with the period known from visual light changes (Fig. 11). Phase estimation is provided by AAVSO data. The velocity curve looks continuous and similar to the observations found for RU Cyg (Hinkle et al. 1997). The amplitude is about 5 km s-1. Good agreement is found between the various wavelength regions. Kiss et al. (1999) have found two more periods in the light changes of TX Dra of 137 and 706 days, respectively. There is no indication for a 137d period in the velocity variations. To check a possible influence of the longer period considerably longer time series of velocity measurements would be necessary. Kiss et al. expect a mode switch in that object around 1999-2000. It would be interesting to monitor the behavior of the velocity variations close to this mode switch.

[FIGURE] Fig. 11. Velocity variations of TX Dra (P[FORMULA]78d). Same symbols as in Fig. 4. The lower panel shows the velocity shift versus phase.

g Her shows velocity variations with an amplitude of approximately 3.5 to 4 km s-1 (Fig. 12). The variations do not follow the mean period, but seem to represent the semiregular changes of the light curve. Comparable trends can be seen in both wavelength regions. A secondary period as indicated by long time AAVSO observations (889 days, Mattei et al. 1997) cannot be excluded, but time coverage of velocity data is not good enough to detect this secondary period.

[FIGURE] Fig. 12. Velocity variations of g Her (P[FORMULA]89d). Same symbols as in Fig. 4.

The velocity variations of RY CrB (Fig. 13) would be one of the largest found within our sample of short period SRVs, if we assume that these variations are due to the stellar pulsation. However, variations clearly do not follow the period known from the visual light curve. Two scenarios could explain the outstanding behavior of this star. First, it could be an unknown double star. Then these variations would be dominated by the orbital motion as evidenced for RR UMi. This hypothesis is supported by Hipparcos measurements. The Hipparcos Catalogue (ESA 1997) lists RY CrB as variability induced mover (VIM), which is a suspected double star system with the brighter component being variable. Further observations of this object would be necessary to verify this hypothesis. The other possibility is a longer "secondary" period, which is the dominant one but has not been observed up to now. Whatever explanation is correct, small, short time scale variations of radial velocity are also observed, so that a description of the behavior has to include both long and short period variation. The velocity curve suggests that the longer period is at least 5 times the GCVS4 period (i.e. more than 450d).

[FIGURE] Fig. 13. Velocity variations of RY CrB (P[FORMULA]90d). Same symbols as in Fig. 4.

Variations of X Her seem to agree roughly with a period half as long as the one from the light variations. Phases were estimated from our own light curve data. AAVSO data had too much scatter for a clearly defined maximum. From our data a velocity amplitude of at least 1.5 to 3 km s-1 can be estimated (Fig. 14). A secondary, significantly longer period of 746d has been found by Houk (1963) and is illustrated in the top axis of Fig. 14. The available data strongly suggest that the velocity of this star varies on both time scales. The total amplitude of the long period variation cannot be determined but seems to be about 4.5 km s-1.

[FIGURE] Fig. 14. Velocity variations of X Her (P[FORMULA]95d). Same symbols as in Fig. 4. Top axis corresponds to the secondary period of 746 days.

For TT Dra we used a rough phase estimation from AAVSO data. The velocity shifts exhibit a nicely shaped variation (Fig. 15, upper panel), that seems to be reasonably periodic (Fig. 15, lower panel). The amplitude is about 3.5 km s-1, and the variations agree well in both wavelength regions. It cannot be decided whether the velocity curve is continuous and comparable to RU Cyg (see Fig. 6 of Hinkle et al. 1997) or discontinuous and thus more like the variations known from miras. This is mainly indicated by the data point close to phase 0 in Fig. 15, lower panel, but the quality of the spectrum at this point is low. However, no line doubling was visible and data from only two cycles were combined here. This object would be highly interesting for further monitoring.

[FIGURE] Fig. 15. Velocity variations of TT Dra (P[FORMULA]107d). Same symbols as in Fig. 4. The upper panel shows the variations plotted versus time. The lower panel shows the variations with phase.

Velocity variations of OP Her are plotted in Fig. 16. The velocity amplitude is approximately 2.5 km s-1. Agreement between the two wavelength regions is similar to other objects of the sample, but the star could not be observed in as many nights as the other stars of the sample, therefore the coverage of the variations is not as good. Variations seem to be somehow cyclic, but may not actually follow the known period. APT observations of this object suggest variations on a significantly shorter timescale of about 50 days. Using 50d instead of 120d seems to fit the observed velocity variations quite good (Fig. 16, lower panel). More (accurate) light curve data are needed to check which one of the two periods is more compatible with the light variations.

[FIGURE] Fig. 16. Velocity variations of OP Her (P[FORMULA]120d). In the upper panel the phase is calculated with the GCVS4 period of 120d, in the lower panel a modified period of 50d (as suggested by recent photometric observations) is used. Same symbols as in Fig. 4.

RV Boo displays a very interesting variation (Fig. 17). Plotting all data into one cycle (lower panel of Fig. 17) the velocity seems to vary quite regularly with a period clearly shorter than the one listed in the GCVS4. Simple analysis of the velocity curve gives a period with 92 or 122 days as the best fit. As three cycles are combined, variations with this shorter period seem to be a regular behavior of the star. It is not clear, whether the period from the visual light variations is different from the one indicated by the velocity variations. A simple explaination might also be that the GCVS period is wrong, i.e. the situation would be probably comparable to that of OP Her. The velocity amplitude of the star is about 3 km s-1.

[FIGURE] Fig. 17. Velocity variations of RV Boo (P[FORMULA]137d). Same symbols as in Fig. 4. The upper panel shows the variations plotted versus time. The lower panel shows the variations with phase (GCVS4 period).

Finally, the object with the longest period in our sample, ST Her , belongs to those short period SRVs where we could follow a well expressed velocity variation in our data in agreement with the visual period (Fig. 18). Phase data are from AAVSO. A velocity minimum is clearly defined around maximum phase. Due to the semiregular behavior visible in the star's light curve it is not surprising that the data observed two cycles later are shifted in phase. The amplitude is about 3 km s-1.

[FIGURE] Fig. 18. Velocity variations of ST Her (P[FORMULA]148d). Same symbols as in Fig. 4.

3.1.2. `Blue' and `red' SRVs

From infrared and visual photometry, Kerschbaum & Hron (1992, 1994) concluded that the semiregular type SRa is not a distinct class of variables but a mixture of mira and SRb classes. They established a new classification scheme dividing the semiregular variables into `blue' and `red' SRVs. Including also the velocity data from the SRVs published in Hinkle et al. (1997) we find that the `red' SRVs have a mean amplitude which is approximately a factor of two larger than the mean amplitude of the `blue' SRVs. The star W Hya, which has the largest velocity amplitude of all SRVs monitored, has been excluded from this calculation as its variability type is uncertain. In the light of this comparison the amplitude of TU CVn, classified as `blue' SRV, is untypically large.

3.2. Absolute velocities of the CO lines

In principle one might suppose that an absolute center of mass velocity for the objects of our sample could be obtained as a mean velocity from the different measurements. All data presented up to now in this paper are velocity shifts relative to a reference observation. Taking into account the observed amplitude of the velocity variations we can compute a velocity of each object in the reference night if we know the center of mass velocity of at least one object and assume that the center of mass velocity is reached at half the velocity amplitude as it is suggested from velocity curves of miras.

However, the whole method is unusable due to the probable incorrectness of the last assumption. The velocity curves of W Cyg and RU Cyg derived from FTS data (Hinkle et al. 1997) indicated already that the velocity of the high excitation CO lines does not necessarily reach the center of mass velocity at any time.

3.2.1. g Her - and a problem

In the light of the problem described above and the lack of reliable standard stars we had to find an independent velocity measurement of at least one object at the time the Coudé Feed spectra were obtained. Fortunately, an FTS spectrum ([FORMULA]v=2 high exc. CO lines) of g Her has been obtained by Ken Hinkle at the 4 m Mayall telescope (KPNO) in the night immediately before one of the observing nights at the Coudé Feed (JD 2449793) and kindly provided to the author. It is known from mira variables that the high excitation [FORMULA]v=2 lines and the second overtone lines of CO show the same velocity behavior. We can now compare the FTS velocity of g Her (Table 2) to the variations observed in the Coudé Feed spectra. As a first assumption we propose that the velocity did not change significantly between the two nights. Although the monitored velocity variations indicate that a change between two nights is quite probable, a different starting point does not seem possible. However, the difference between two nights is typically not larger than 300 m s-1. In the Coudé Feed velocity curve for g Her the relevant data point represents a velocity shifted from the velocity maximum observed in wavelength region 1 by only 0.1 km s-1. We can therefore assume that the FTS (absolute) velocity represents almost the maximum velocity observed for the high excitation [FORMULA]v=2 CO lines or the [FORMULA]v=3 CO lines, respectively. On the other hand, the FTS velocity is about 0.4 km s-1 less than the center of mass velocity derived from circumstellar CO radio emission. Taking into account all uncertainties in the Coudé Feed (wavelength region 1), the FTS and the radio velocity we find that the center of mass velocity is hardly reached by the observed Coudé Feed velocities at any phase. The amplitude in wavelength region 2 is a little bit larger but still a significant asymmetry between outflow and infall remains. Unfortunately it is not clear whether we really strongly underestimate the amplitude in region 1 or not.


Table 2. Radial velocities derived from FTS spectra of g Her, X Her and RR UMi obtained on March 14, 1995

3.2.2. Other objects

What can be done to get more insight into this question, is to measure the velocity of each object in our sample in the night JD 2449793 and then derive the velocity range for each object. Under the assumption that the velocity of g Her in that night is equal to the FTS velocity we correlated all stars of that night with g Her. Additional correlation was done with the secondary standards UW Lyn, ST Her and µ Gem. The selection of these objects was made deliberately. These three stars cover most of the range of radial velocities of the members of our sample. As a result, for almost every star we have such a template that the resulting pixel shift in the correlation is small, which reduces the error of the velocity derived by correlation. Furthermore, two of the objects were observed in the beginning of the night, ST Her and g Her after midnight. The scatter of the velocities derived from these four objects could therefore help to estimate the influence of the absolute pixel shift on the accuracy of the derived velocities. The current velocity of these stars was determined by correlation with g Her.

The results of this correlation are given in Table 3. For each star the velocity given is the average of the velocities relative to the four standard objects with the exceptions of a few objects where the velocity shift was too large for some of the templates and therefore gave no reliable result. The standard deviation derived from the four templates is given and indicates the error of the correlation method. The agreement between the values from the four templates is impressively good.


Table 3. Attempt to derive absolute velocities for the SRVs observed with NICMASS for JD 2449793. Velocities have been calculated using the correlation technique as described in the text. The template for the correlation was g Her adopting an FTS velocity. ST Her, UW Lyn and µ Gem were used as secondary templates. The second column gives the mean velocity derived from the four standards with the standard deviation listed in Column 3. Columns 4 and 5 give the respective observed maximum and minimum velocity calculated from the relative RV variations in wavelength region 1; the latter were determined by using the velocity shifts relative to JD 2449793. Column 6 gives the velocity value found in the literature. Column 7 lists the source of the literature value (TCO...thermal CO (Kerschbaum & Olofsson 1999), GC...General Catalogue of Stellar Radial Velocities (Wilson 1953), LZ...see text). Column 8 and 9 give the difference between literature value and the maximum and mean observed Coudé Feed velocities, respectively. All velocities are heliocentric and in km s-1. Stars are sorted by constellation. Only one template could be used for X Her due to the star's high system velocity.

We calculated from this reference point the minimum and maximum velocity measured in wavelength region 1. A comparison with velocity data from the literature is given in Table 3. For a number of stars of our sample we measured the radial velocity with the Coudé Feed in the blue region around 4300 Å. These measurements were obtained on March 30 1995 (JD 2449806). The accuracy achieved is about 1.5 km s-1. If there was a large difference between the literature value and our blue velocity, the latter one is listed in Table 3, which is indicated by "LZ" in Column 7 of that table. We found differences between the literature values and our data of up to 10 km s-1.

Some objects show very large differences between the literature value and the derived velocity on JD 2449793. These cases can be explained quite well either as double stars (RR UMi and o1 Ori), suspected double stars (RY CrB) or large amplitude variables (R Leo).

A closer look at the velocity differences listed in Table 3 (Columns 8 and 9) shows that for several objects the maximum Coudé Feed velocity is less than the literature value. The difference, however, is always below 1 km s-1. This is also valid for those objects that exceeded at some phase the velocity listed in the literature, which means that the literature value is very close to the maximum value observed. The only exception is X Her, which is probably due to a secondary period.

The difference between literature value and Coudé Feed velocities gets even more obvious when comparing the mean Coudé Feed velocity (wavelength region 1) instead of the maximum velocity. The results are listed in Table 3 (Column 9). All differences are negative, on the average about 1.2 km s-1 (ignoring the objects with large velocity differences noted before). In fact, this means that there is a significant asymmetry between the outflow and infall relative to the center of mass velocity (if the latter is represented by the literature values) in all objects of our sample. This common behavior suggests that it is not due to chance. Possible explanations will be discussed in Sect. 4.2

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999