In Table 5 we compare our orbital elements with previous determinations. For most parameters the present results are consistent with the earlier determinations except that the high quality of our observational data and the good coverage of the orbital period allows to tighten the errors. The only controversial values are the period and the velocity amplitude of the O star. We have pointed out in Sect. 3 that once the deviating value by Niemela & Sahade (1980) is recognized as due to a calculation mistake, all period determinations agree within their errors.
Table 5. Comparison of the orbital elements given in the literature with the present results.
Regarding the radial velocity amplitude of the absorption lines we have identified the reason for disagreement. In Sect. 4.2 we have demonstrated that a direct fit to the absorptions without correcting for the influence of the WR emission leads to amplitudes as large as reported by Niemela & Sahade (1980) and Moffat et al. (1986). The semi-amplitudes of Ganesh & Bappu (1967) and Pike et al. (1983) agree with our new value. However, their papers do not mention that they have corrected for the influence of the WR emission. Therefore, the agreement is probably fortuitous.
In Sect. 6 we have reported a phase shift of the C III /IV emission. Our interpretation of the phase shift is somewhat disturbing in view of a possible systematic influence on the accuracy of the other orbital elements. If the apparent periastron date can be shifted by additional emission from a region not associated with the WR star, what about the eccentricity and the amplitude? In fact, more in line with this expectation is the orbital curve of the He II . If its radial velocities are plotted together with that of other lines then it is obvious that its deviating eccentricity is clearly significant. From the point of view that there is additional emission that disturbs the radial velocity, the most surprising result is that the orbital curve of the C III/IV fits so perfectly with that of the other lines. For this line the only signature of the hypothetical influence is a phase shift.
The observations contain further unexplained effects that could influence the orbital solutions. We observe an erratic behavior of some lines (not all!) during our 1995 observations. The most extreme case among the lines we have measured is C IV . In Fig. 9 we show the phase diagram of this line. It is evident that the velocities from the 1995 observations are highly disturbed. Another example is C IV . For the C IV line we find a less extreme but still significant deviation of the 1995 data to more negative values than the orbit solution. The other lines listed in Table 1 do not show a disturbance. Their 1995 data are in perfect agreement with the 1996 observations in that both data sets yield the same distribution and RMS deviation from the orbital solution.
We note that despite the disturbing observations reported above we find consistent orbital elements from all lines, except for the periastron date and periastron angle. Therefore, the main results of our investigation, the velocity semi-amplitudes, appear not to be affected. Nevertheless, we cannot exclude that the systematic errors could be larger than the errors we report in Table 5. Unfortunately, we have no means to quantify our words of caution.
The most significant difference of the parameters derived here to previous determinations is the amplitude of the O star's orbit. We measure a value that is almost a factor of two smaller than that of Niemela & Sahade (1980) and Moffat et al. (1986). Consequently, we derive a much lower mass for the Wolf-Rayet star. Previously, it was commonly assumed that the WR star has a mass of . With this mass the WR should have a luminosity of (Smith et al. 1994), which is a factor of 10 higher than the luminosity obtained by the spectroscopic analysis of Schaerer et al. (1997). This disagreement is definitely too large. The mass implied by the WR's luminosity using the mass-luminosity relation for WR stars is (Schaerer et al. 1997). This value is lower than the mass derived in the present analysis, . However, Howarth & Schmutz (1992) find that the luminosities of Wolf-Rayet stars derived from their masses are systematically higher by about a factor of two than the luminosities obtained from spectroscopic analyses. Therefore, the disagreement between 5 and 9 is not unusual.
The most unfortunate aspect of the present investigation is that the determination of the inclination involves results from spectroscopic analysis and stellar evolution calculations. It would be preferable if fundamental stellar parameters could be used to test these calculations. We hope that in the future there will be sufficiently precise polarization observations to confine the inclination. We estimate that the polarization measurements need to be more precise than the existing data by about a factor of 5. The open question is whether there is intrinsic variability of the polarization that prevents results with this accuracy.
A long period system like Vel is not easy to observe. It was a considerable effort to obtain the observations presented in this paper. We were rewarded by a set of spectra of excellent quality that allowed us to measure the orbit of Vel with higher precision than before. Our results confirm the orbital elements obtained by Pike et al. (1983), but now we also understand the origin of the contradictory results obtained by Niemela & Sahade (1980) and Moffat et al. (1986).
© European Southern Observatory (ESO) 1997
Online publication: March 24, 1998