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Astron. Astrophys. 361, 167-174 (2000)

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3. Results

In Figs. 1 to 9 we plotted the velocity variations on top of the light variations. For some stars single velocity data points from a few years earlier exist. These were not included in the plots to allow for a larger scale on the time axis. A mean velocity of the star - when available - has been subtracted from the velocity values. The velocity used for subtraction is given in the figure caption. Lebzelter (1999) found that thermal CO velocities and other values from the literature all appeared to share the same property, i.e. a systematic offset in the sense that the IR CO lines are blueshifted for all or a large part of the lightcycle. We will come back to this point in the discussion of the results. Note that some of these stellar velocities have been derived from blue/optical spectra and may therefore not be representative of the center-of-mass velocity. For miras it has been shown that the blue/optical velocities are shifted several km s-1 positive of the center-of-mass velocity (Reid 1976, Hinkle & Barnes 1979). Wallerstein & Dominy (1988) found for 5 semiregular variables without H2O masers that on the average there is no velocity shift between optical and thermal (=systemic) velocity. However, for 4 SRVs in their sample showing H2O maser emission a difference [FORMULA] - [FORMULA] of -1.3 km s-1 was found. It is therefore not clear whether the optical velocity is representative for the center-of-mass velocity or not.

[FIGURE] Fig. 1. Light and velocity variations of V450 Aql. Filled circles mark velocity measurements (right axis). No error bars are given as the error bar would be typically of the size of the symbols as can be easily seen from Table 2. The stellar velocity (-51.3 km s-1 from blue/optical spectra, see text) has been subtracted. To allow a better comparison velocity axis is in reverse order. Light curve data points are labeled with crosses.

[FIGURE] Fig. 2. Light and velocity variations of SV Cas. For this star no center-of-mass velocity is available in the literature. Therefore absolute velocity values are plotted. Same symbols as in Fig. 1.

[FIGURE] Fig. 3. Light and velocity variations of W Cyg. Stellar velocity (-14.4 km s-1 from thermal microwave CO, see Hinkle et al. 1997) has been subtracted from the velocity data. Same symbols as in Fig. 1.

[FIGURE] Fig. 4. Light and velocity variations of RU Cyg. Stellar velocity (-6.3 km s-1 from thermal microwave CO, see Hinkle et al. 1997) has been subtracted from the velocity data. Same symbols as in Fig. 1.

[FIGURE] Fig. 5. Light and velocity variations of the short period mira RT Cyg. Stellar velocity (-118 km s-1 from blue/optical spectra, see Lebzelter et al. 1999) has been subtracted from the velocity data. The arrows indicate the phase of line doubling. Same symbols as in Fig. 1.

[FIGURE] Fig. 6. Light and velocity variations of TX Dra. Stellar velocity (46.4 km s-1 from blue/optical spectra, see Lebzelter 1999) has been subtracted from the velocity data. Velocity has been measured in two wavelength regions (see text). Wavelength region 1 is marked by filled circles, wavelength region 2 by open circles.

[FIGURE] Fig. 7. Light and velocity variations of g Her. Stellar velocity (1.4 km s-1 from thermal microwave CO, see Lebzelter 1999) has been subtracted from the velocity data. Same symbols as in Fig. 6.

[FIGURE] Fig. 8. Light and velocity variations of ST Her. Stellar velocity (-22 km s-1 from thermal microwave CO, see Lebzelter 1999) has been subtracted from the velocity data. Same symbols as in Fig. 6.

[FIGURE] Fig. 9. Light and velocity variations of W Hya. Stellar velocity (38 km s-1 from thermal microwave CO, see Hinkle et al. 1997) has been subtracted from the velocity data. Same symbols as in Fig. 1.

However, as thermal CO velocities are missing for many objects, the velocities used here are the only external source of velocity information available. Keeping the above mentioned uncertainty in mind we will use this velocity value as systemic velocity. We note that an investigation of a systematic velocity shift between blue and thermal CO velocities is still missing for semiregular variables. To avoid confusion we will add a remark on the source of the velocity in the figure caption (thermal CO or blue/optical). For the reference of each velocity we refer to the paper listed in Table 1.

The velocities have been plotted in reverse order (largest velocity at the bottom) for the sake of an easier comparison of velocity and light variations. Throughout this paper positive velocity relative to the systemic velocity means that the material is moving toward the star and hence away from the observer. Furthermore the scale of the velocity axis has been adjusted to have an overlap between velocity and light curve.

It is obvious that the light and velocity variations are well correlated in all objects of our sample. Some - but not all - changes in the light amplitude are well represented in the behavior of the velocity curve as well. All stars reach their smallest difference to the systemic velocity at or close to light minima, while the minimum velocities are correlated with light maxima.

V450 Aql exhibits velocity changes with an amplitude of about 1.6 km s-1. This is the smallest variation in our sample and one of the smallest among the stars for which Hinkle and collaborators monitored CO velocities. The accuracy of the velocity measurements is high enough to ensure that the star is truly variable in velocity. However, due to the small amplitude the uncertainties in the light curve and the sampling of our velocity measurements makes comparison of light and velocity curve rather difficult (Fig. 1). Although it seems like V450 Aql behaves the same way as all the other stars, even the opposite behavior (i.e. maximum velocity at maximum light) cannot be excluded.

Line doubling is present in the short period mira RT Cyg (Fig. 5) significantly before the visual light maximum. If we compare the behavior of this star with the velocity curve of [FORMULA] Cyg, we have to keep in mind that RT Cyg has a very symmetric light curve compared to its long period counterpart. The slight phase shift between the minimum velocity and the light maximum found in [FORMULA] Cyg is not visible in RT Cyg. However, it is possible that the phase coverage is not adequate to detect such a small shift (which we would expect to be only a few days due to RT Cyg's short period). Light curve data do not allow a determination of the exact date of minimum around JD 2446200. Still the line doubling observation with the maximum velocity observed seems to be located clearly after the light minimum in agreement with the pattern seen in [FORMULA] Cyg. The single velocity measurement two cycles later fits very well onto the light curve as well indicating that the correlation of light and velocity curve is not limited to the well covered period.

The data for SV Cas (Fig. 2) also merit further comments. The behavior of this star was difficult to interpret without the light curve. Plotting all data into one cyle made Hinkle et al. (1997) suspect that the star might have a velocity curve similar to the miras, i.e. discontinuous. Our result shows that this interpretation is not necessary, because the velocity variations follow the semiregular light variations quite well. It was incomplete phase coverage of the velocity observations that led to the misinterpretation. The three maxima visible in Fig. 2 give a mean period of only 237 days, somewhat less than the GCVS4 value used by Hinkle et al.

The comparison of parallel velocity and light variations is of similar importance for the understanding of the velocity variations in the case of ST Her (Fig. 8). Lebzelter (1999) assumed a phase shift between the velocity measurements around JD 2450150 and earlier data points to explain that the velocities did not fit into a simple phase diagram. Fig. 8 shows that this assumption was correct and that the star is not following its mean period around that day. However, the velocities around that time fit well onto the observed light curve.

For four additional stars (RV Boo, RR CrB, X Her, and TT Dra) velocities are available but good light curves are not, making a detailed comparison, as for the stars in Table 1, impossible. Using available light curves, we attempted to confirm that these stars behave as the stars with good light curves. All of them seem to exhibit the same kind of correlation between light and velocity changes.

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© European Southern Observatory (ESO) 2000

Online publication: September 5, 2000
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