Astron. Astrophys. 318, 819-834 (1997)

4. Radial velocity and line-profile variations

4.1. Photospheric lines

All absorption lines are influenced by the stellar wind and show asymmetric deformations on their violet wings (e.g. by Wolf & Appenzeller (1979) in the case of  Sco). The asymmetries of the lines are indicators of a photospheric velocity gradient.

The velocity and intensity variations occur in the cores of the photospheric lines. So we refer to these variations as photospheric disturbances, even if a closer look reveals that most lines are shifted bluewards by the velocity gradient in the line-forming regions. Assigning an average velocity to every line, the weakest lines like OII 4705 (80 mÅ) have the smallest velocities. The depth structure of the atmosphere can be analyzed using lines of different strength.

The photospheric variability pattern is very similar in different lines, as can be seen in Fig. 3. A pulsation-like pattern is visible in the first 60 days of this run. It disappears later on and changes to a quite random pattern. This variation can be seen in all three program stars but is never observable for more than a few "cycles". The pattern is clearly shifted in time and velocity between various lines. This is shown in Fig. 4 for three absorption lines in the spectrum of  Sco.

Fig. 3. The velocity variations of the line centers in  Sco in 1993. The central position of the line was measured by fitting Gaussians to the profiles. The sequence shows the radial velocity for OII 4705, NII 4601, HeI 4921, and

Fig. 4. The velocity variations of the line centers in  Sco. The sequence shows the shift in time and velocity of the pattern for AlIII 5696, HeI 4921, and

A cross-correlation analysis of the velocity shifts indicates the propagation of disturbances through these layers. For this purpose the velocity curve of each line is splined to obtain equally spaced points for each spectral line. The resulting curves are shifted to a mean value of zero and their variance is normalized to unity. The variations in the photospheric lines are cross-correlated with those in a reference line. The AlIII 5696 line was adopted as reference since it gives the highest correlation coefficients. The position of the maximal correlation value gives the time-shift between both patterns. The correlation coefficients can be used to remove non-significant points. Only points with a correlation coefficient greater than 0.6 are taken as significant. The result is shown in Fig. 5 for each of the three stars.

Fig. 5a-c. The figure shows the propagation of disturbances in the line cores of photospheric lines. The dotted lines indicate the systemic velocities derived from pumped FeIII lines

The points for  Sco in 1995 are not shown because the AlIII 5696 line was not observed in this year. Nevertheless, the use of another reference line leads to the same curve except for an offset in time. The offset is of the order of the delay between the variations of AlIII 5696 and those of the new reference line obtained in earlier years.

Our analysis shows for the first time that disturbances which affect the wind of early-B hypergiants are generated very deep in the photosphere (or even in sub-photospheric layers). Presumably, they are causally connected to the pulsation-like motions as shown by the pattern of the radial-velocity variations of the photospheric lines. However, a simple and straightforward connection could not be found.

In order to derive the velocity law in the photosphere and the deep wind layers from the relations shown in Fig. 5, the formation depth of the lines have to be known from hydrodynamical photospheric models.

We estimate the amplitude of the radius variations of the photosphere from the integration of the radial velocity curves below.

4.2. Wind profiles

In the stronger P Cygni-type profiles like and outwards propagating absorption features are detectable. Due to the strong emission, these features are invisible at expansion velocities below about . This can be seen in Figs. 18 and 19, upper panels. In lines showing less emission, e.g. , the visibility of these features at low velocity is normally disturbed by the strong photospheric absorption line and its variability.

If we assume that the discrete absorption features are due to clumps of gas moving with the ambient wind, they can be used to derive the velocity law in the wind. In order to trace back the velocity law to photospheric velocities we searched for fainter P Cygni-type profiles. In such profiles the absorption features can be followed down to low velocities. The FeIII 5127 and FeIII 5156 lines have weak P Cygni-type properties as shown in Fig. 6.

Fig. 6. Weak P Cygni-type profiles of FeIII lines in the program stars. The synthetic photospheric profiles were calculated using the code introduced in Sect.  3

In these lines the propagating components are remarkably distinct down to very low velocities. This is shown for  Sco in the dynamical spectrum of Fig. 7. Four events are visible in 1993. If we trace these events we get velocity curves which can be compared to -type velocity laws (Eq. (3)). The result is shown in Fig. 8.

Fig. 7. Dynamical spectrum of the FeIII 5156 line in  Sco in 1993. The single spectra have been divided by the mean profile

Fig. 8a and b. The acceleration of absorption features through the wind. The symbols shown here have been measured using the FeIII 5127 , FeIII 5156 , HeI 6678 , HeI 5875 , and lines. The dotted lines indicate in the heliocentric system. The data plotted in Fig. 5 have been shifted in time and are included as dots for comparison. A velocity law with , , and has been superimposed on the curve for  Sco and shifted by , so it starts at

Such features are notable in both other stars, as well. However, for HD 169454 the coverage of the monitoring was not dense enough to establish a curve like in Fig. 8.

The curves in Fig. 5 and Fig. 8 show nearly the same gradient in the velocity domain around 60 . Hence it is likely that the features we trace in the wind lines (Fig. 8) are causally connected to the photospheric variability. Fig. 8 indicates that the discrete absorption components have a velocity law similar to that of a law with . However, the velocity law of the ambient wind of our program stars might not have , because the density clumps which produce the features may not move with that ambient wind. If the features are due to weak density perturbations in the wind, they can travel with the sound speed through the wind. It should be noted that this speed is different from the sound speed in the stellar atmosphere (Abbott 1980). On the other hand, if the density perturbations are large enough to block radiation from the star in the UV resonance lines that drive the wind, their acceleration can be significantly smaller than that of the ambient wind. Therefore =2.5 can be considered as an upper limit to the velocity law.

Similar results were obtained for O-stars, where discrete absorption components were investigated by numerous authors. The propagation of these DACs was traced from to for several stars in the optical range (e.g. Prinja & Fullerton 1994, Massa et al. 1995, Prinja et al. 1996).

4.3. Variability of the P Cygni emission components

As can be seen in Fig. 9, the equivalent widths of the emission lines are variable. Most remarkable the variation pattern is visible in all wind-emission lines; in those formed in the inner regions of the wind (HeI 6678) as well as in lines formed out in the wind like .

Fig. 9. The variations of the maximum emission flux in units of the continuum of several lines in  Sco in 1993. The flux was measured by fitting Gaussians to the emission part of the profile. The typical variation pattern can only be seen in lines with wind emission. "Photospheric emission lines" like SiII 6347 remain largely unaffected

We now analyze the emission variability by cross-correlation. Instead of comparing the radial velocities, we correlate the height of the emission components. In contrast to the absorption, the emission radiation originates in the whole envelope. So only a sequence in time, but no velocity information can be derived using this method. If the observed time shifts are due to the propagation of density variations through the emitting envelopes of different lines, these envelopes cannot differ much in radius, since the time shifts are rather small.

Table 4. Time shifts between the emission variability for  Sco . was used as reference line. The HeI 6678 emission was too weak in HD 169454 and HD 190603 to give reasonable correlation functions

No correlation could be found by comparing the emission variability with the propagating components seen in absorption. For  Sco the typical time scale in the emission variations is about 15 days, which is shorter than the repetition time of the absorption features of approximately 24 days.

This argues against a connection between the variations seen in emission and in absorption. The emission variability might be connected to the photometric variations reported by Burki et al. (1982) and Sterken et al. (1997) who found periods of up to 16 days.

So far the variation patterns of the photospheric lines were used as tracing probes through the photospheric layers. However, a closer look on these pattern reveal some interesting behavior. We integrated the radial-velocity curve of a typical line like NII 4601 after subtracting the mean radial velocity. The emission variability is found to be correlated with the resulting values of the integrated radial velocity.

In Fig. 10 we show this by plotting the -emission flux versus the integrated quantity. Years, where the integrated radial velocities show less correlation with the -emission variability, like  Sco in 1994 and 1993, the behaviour might be due to wind influences. So in the 1993 plot for  Sco the relation clearly splits due to the minimum of the photospheric velocity at (Fig. 3). In contrast to the other peaks, this one shows no correlation with the emission. So this peak might be caused by the wind variability rather than by the typical photospheric variability.

Fig. 10. The emission plotted versus the integrated radial-velocity variations

Using the propagation law derived in Fig. 8, the propagation of this peak coincides well with the early flank of the strongest observed absorption feature. The center of this absorption feature is seen in the FeIII 5127,5156 lines about 10 to 12 days later. In our model described below, this peak in velocity coincides with a phase of sharply increasing wind density starting at model date (Fig. 17).

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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