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Astron. Astrophys. 328, 219-228 (1997)

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3. The orbital period

There are two papers comparing radial velocity data of [FORMULA]  Vel over a long time span. Pike et al. (1983) re-measured plates obtained between 1904 and 1913, and 1955 and 1959. They derive a period of [FORMULA] days. Niemela & Sahade (1980) compare observations of 1919 with data from 1962. They find a phase shift of 3 days if [FORMULA] d is assumed. From this difference they calculate a new period of [FORMULA] d. However, their result is not correct. Between the observing dates there are only about 200 orbits, which yields [FORMULA] d. Although we cannot reconstruct how they arrived at their conclusion, we note that Niemela & Sahade (1980) comment: "... orbital solutions for periods ranging between 78.49 and 78.53 days are compatible with our data, and neither one of them is completely ruled out." In any case, if correctly calculated, the period of Niemela & Sahade (1980) is consistent with that of Pike et al. (1983).

In Fig. 2 we compare our orbital solution for the H9 absorption

[FIGURE] Fig. 2. Observed radial velocities of absorption lines. Crosses and plus signs denote measurements of H9 during 1995 and 1996, respectively. The stars represent mean absorption line velocities of H [FORMULA] through H10 obtained between 1904 and 1913 and the triangles indicate the values obtained between 1955 and 1959 (adopted from Pike et al. 1983). The line is the orbital solution fitted to the combined data set with a period [FORMULA] days.

(Sect. 4.2) with absorption line velocities from the years 1904 - 1959. The data have been published by Pike et al. (1983). It is obvious that there is a shift of about 10 [FORMULA] between the velocity curve as defined by Thackeray's data (triangles) and by our velocities. Luckily, the distribution of Thackeray's data is such that the epoch of maximum radial velocity is nearly independent of the value of the systemic velocity. However, the older data of Mills expedition (stars) are sensitive to a difference in [FORMULA] -velocities and therefore, the Mills data set is of less value for the determination of the period. We derive a best fit of [FORMULA] d, where the relatively large error allows for an unknown shift in systemic velocities between the data sets.

The radial velocities of the P Cygni absorption of He I   [FORMULA] forms a saw-toothed pattern (cf. Fig. 1 of Niemela & Sahade 1980). Repeating the approach of Niemela & Sahade (1980), we compare our data with that of Perrine (1920) using a period of 78.5 d. We find a phase shift of 8 days. The time difference between the observations is 357 orbital periods and we obtain [FORMULA] d. The error estimate is obtained by including the data set of Niemela & Sahade (1980) (see above). The problem with this method is that the P Cygni absorption is a feature formed in the wind. More exactly, we use the fast transition from a slow wind to a fast wind around phase 0 to align the 1919 data with our data set. As shown in Fig. 3 this transition is exactly

[FIGURE] Fig. 3. Comparison of the variations of the observed velocity of the P Cygni absorption of He I   [FORMULA] with the variation of the X-ray flux. Crosses and plus signs denote measurements of the P Cygni absorption during 1995 and 1996, respectively, and the squares mark the values reported by Perrine (1920). The velocities are measured in [FORMULA] relative to the heliocentric rest-frame. The stars indicate the X-ray flux in units of milli-cts s-1 shifted down by 500 milli-cts s-1 (Willis et al. 1995).

related to an increase of the hard X-ray flux (Willis et al. 1995). Therefore, the time dependence of the variation of the terminal velocity is probably related to the opening angle of the bow shock, similarly to the interpretation of the X-ray variability (Stevens et al. 1996). Such a phenomenon is likely to show cycle-to-cycle variations.

The two period determinations yield results that are only marginally consistent. We have identified reasons to suspect systematic effects in both approaches and therefore, the agreement is satisfactory. As we have no arguments to favor one method over the other we adopt the mean: [FORMULA] d.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998