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

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4. The velocity amplitudes

4.1. The emission lines

The emission lines have a full width at zero intensity corresponding to 3000 to 5000 [FORMULA]. It is not straightforward to extract a velocity amplitude of 200 [FORMULA] from lines of more than ten times this width. In order to measure the radial velocity we have fitted Gaussian profiles to the emission lines. The only exception is the line complex C III/IV [FORMULA] Å which is not well represented by a Gaussian. We measured the line shifts of the C III/IV [FORMULA] emission with a cross-correlation method. However, the main difficulty in measuring radial velocities arises not from the line widths but from the variability of the line shapes. Part of the line profile variations, such as the line widths, are clearly systematic. Other changes appear to be stochastic.

In Table 1 we summarize the orbital solutions obtained for individual emission lines. We minimize the sum of the squared deviations by varying simultaneously all free parameters. Besides the orbital elements the fit yields also the RMS deviation. We find that there are lines that show a higher degree of variability whereas others are fairly well behaved.


[TABLE]

Table 1. Orbital elements determined from the radial velocity variations of different emission lines. A period of [FORMULA] d is assumed and only the 1996 data are analyzed.


We identified six lines that define the orbital motion with a RMS scatter of less than 20 [FORMULA]. As an example we display in Fig. 4 the radial velocity curve of C III /IV   [FORMULA]. In Table 1 we list an identification for the features but we do not attempt to derive the systemic velocity from these lines because the centers of the emissions are red-shifted by an amount that depends on the individual transition.

[FIGURE] Fig. 4. Phase diagram of the radial velocities of the C III /IV line complex at 4650 Å. Plus signs denote our 1996 observations and the diamonds the 1995 data.

The RMS scatter of H [FORMULA] is twice as large as for the other lines. The reason is that superimposed on the H [FORMULA] emission there is a strong absorption feature that originates in the spectrum of the O star. We have fitted H [FORMULA] simultaneously with two Gaussian profiles, one for the emission and the other one for the absorption. We show an example in Fig. 5. Although the fit to the red wing is not perfect the observed profile is reproduced nicely by the double-Gauss fit.

[FIGURE] Fig. 5. Fit of a double-Gauss profile to the observed spectrum of H [FORMULA]. The two Gauss-components are represented by the two dashed curves and the combined profile is indicated by dots.

It is not surprising that the radial velocities are more uncertain when two independent wavelength shifts and line strengths have to be determined simultaneously. However, it is essential to include the absorption feature when the radial velocities are measured. In order to demonstrate this point we have included in Table 1 two solutions for He II   [FORMULA]: one obtained with a single-Gauss fit, the other with a double-Gauss fit. The amplitude from the single-Gauss solution disagrees on a 6 [FORMULA] level from the mean amplitude of the other lines. The relative strength of the absorption feature when compared to the emission is much less for He II   [FORMULA] than for H [FORMULA]. Nevertheless, the He II   [FORMULA] absorption is sufficient to systematically shift the center of the emission feature such that a lower amplitude is measured. Niemela & Sahade (1980) and Moffat et al. (1986) have obtained a semi-amplitude for He II   [FORMULA] consistent with our single-Gauss fit. Both have omitted this line from the average orbital solution because "... this line often deviates in a similar way in other W-R binaries." We now understand the reason for the odd behavior of this line. As demonstrated, the influence of the absorption can be corrected such that He II   [FORMULA] yields orbital elements that agree with those from lines that are free from absorption features.

As the deviation of the He II   [FORMULA] single-Gauss fit is systematic, we have excluded the elements of this solution from the average. We also exclude the He II   [FORMULA] result because due to the large correction for the relatively strong absorption, the elements for this line are more uncertain. With the six remaining solutions we determine a radial velocity semi-amplitude for the Wolf-Rayet star of [FORMULA] [FORMULA]. The six lines have an RMS error of 3 [FORMULA].

With about 50 measurements around the phases with maximal amplitude, each line solution yields an amplitude accurate to 1/7 of its RMS-scatter. Thus, we expect the semi-amplitudes of each individual solution to be accurate to 1.5 to 2 [FORMULA] (see Table 1). The standard deviation of the six values from the mean is larger than our estimates of the errors of the individual solutions. We suspect that there are systematic effects that we are not aware of and that the six results are not distributed randomly. Therefore, we refrain from reducing the error of the mean amplitude by a factor of [FORMULA], which would give an error of 1.2 [FORMULA]. Instead, we adopt the expected error of a solution for an individual line, i.e. we adopt [FORMULA] [FORMULA]. With the quoted precision we have allowed for some of the systematic effects on the amplitude.

4.2. The absorption lines

Within the wavelength coverage of our observations, all absorption features are blended by at least one emission line. In the simplest case of an absorption blended by the corresponding emission, the absorptions are superimposed on the steep sides of the WR emission during the phases of maximum radial velocity. The underlying slope of the emission shifts the line center towards the line wings. Measuring directly the center of the absorption features will overestimate the maximum positive as well as the maximum negative velocities. Thus, if no correction for the WR emission is made then inevitably too large amplitudes will be measured. In Table 2 we list the orbital elements obtained without correction for the emission blend. Depending on the strength and form of the WR emission we find velocity semi-amplitudes as large as 67 [FORMULA]. With the understanding that these values are too large, they yield an upper limit for the O star's velocity amplitude. We note that Niemela and Sahade (1980) and Moffat et al. (1986) have measured semi-amplitudes of 70 [FORMULA] and 83 [FORMULA]. From the upper limits of the uncorrected measurements in Table 2 we can qualify their results as being systematically too large. In particular, the results from H [FORMULA] and H9, for which we find fit solutions with a very small intrinsic RMS scatter, set a very stringent upper limit to the orbital velocity of the O star: [FORMULA] [FORMULA].


[TABLE]

Table 2. Orbital elements determined from absorption lines adopting [FORMULA] d and [FORMULA]. No correction for the influence of the WR emission is made.


Although it is clear that we must correct for the WR emission, it turns out that in practice this task is far from trivial. Some lines are blended by several other lines such that the blending problem is so severe that it is hopeless to define a reliable correction. Unfortunately, the two lines with the best RMS scatter belong to this category. Inspection of the wavelength regions around H [FORMULA] and H9 reveals multiple line blends. We believe that their good RMS scatter testifies to only small disturbances by WR features. However, we know that there are He II emissions at the wavelengths of the hydrogen absorptions, even though they cannot be isolated among the lines that contribute to the blends.

In order to take into account the WR emission we have tried several approaches. In Table 3 we give results obtained by double-Gauss fits and by subtracting a mean emission profile with the absorption removed shifted according to the WR orbital elements. In both cases we find that the intrinsic variations of the emission line profiles limit the accuracy of the results. This is obviously the case when we subtract a mean profile. But also the double-Gauss fit suffers from the variations because sometimes the line shapes are clearly less well reproduced by Gauss profiles. In addition, any correction is subject to systematic errors and we cannot exclude the possibility that our approach introduces systematically too large corrections. As we can only correct for isolated line emissions we are left with only five lines to derive the elements of the O star. We find [FORMULA] [FORMULA], where we have given single weight to He I   [FORMULA] and to the means of the two results for HeI   [FORMULA] and H [FORMULA], and a smaller weight for HeII   [FORMULA] corresponding to their squared RMS-deviation relative to that of the other lines. The given error is the standard deviation defined by the five results. In view of the difficulties in measuring the absorption-line amplitudes, an error of 2 [FORMULA] is uncomfortably small. However, we know no better method for deriving a more reliable error estimate. Again, as for the emission lines, we refrain from reducing the error by the square root of the number of measurements because we do not believe the results deviate randomly from the correct amplitude.


[TABLE]

Table 3. Orbital elements determined from absorption lines adopting [FORMULA] d, [FORMULA], and [FORMULA]. The influence of the WR emission is taken into account with method a, b, or c.


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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998

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