4 Is HD108 a spectroscopic binary?

Using the rest wavelengths listed in Table 3, we determined the radial velocities by fitting Gaussians to the bottom (top) end of the absorption (emission) lines. The radial velocities (RVs) of the He II $\lambda \lambda$4200, 4542 lines are summarized in Table 2, together with the RVs of the N III $\lambda \lambda$4634, 4641 and He II $\lambda$4686 emission lines. We have used the generalized spectrogram technique of Heck et al. (1985, hereafter HMM) and the trial method of Lafler & Kinman (1965) to search for periodicities in the He II $\lambda \lambda$4200, 4542 RV time series. For the HMM method, we evaluate a rough estimate of the significance level (SL) by $SL = {\rm e}^{-\frac{P}{\sigma^2}}$ where P is the periodogram amplitude and $\sigma$ the rms dispersion of the data. We will consider that a period is significant if its SL is less than 0.01.

 

 

Table 3: Adopted rest wavelengths of the lines used to compute the RVs displayed in Figs. 2-4 and listed in Table 2.

Ion	Effective	Nature
	wavelength
He II	4199.830	Abs.
He II	4541.590	Abs.
Si III	4552.654	Em.
Si III	4567.872	Em.
N III	4634.250	Em.
N III	4641.020	Em.
He II	4685.682	Em.

4.1 Short-term variability

Over all those years of intense study of HD108, only a few authors really addressed the issue of short-term variability of this star, even if most of the periods found were rather short. For instance, Vreux & Conti (1979) obtained two spectra per night during two consecutive days of their observing run. However, to analyse completely the short-term variability, more spectra taken on numerous consecutive days are needed. To investigate this problem, we collected at least two spectra per night during the 7 days of the August 1987 run and during the 6 days of the November 1998 run. The 1987 data cover the He II $\lambda$4200 line, while the 1998 data cover the He II $\lambda$4542 line. These data enable us to search for short-term variations of the spectra, and also to check the short periods (a few days) given in the literature. Because of the poorer spectral resolution (1.7Å) of the 1987 data, the RVs show a large scatter in 1987 compared to the 1998 measurements that were obtained with a resolution of 0.2 Å (see Figs. 2 and 3).

We tried to search for a periodicity in the He II RVs measured on the two sets of data (20 spectra in 7 days + 15 spectra in 6 days), but we did not find any significant short period. Moreover, those data do not confirm the periods given in the literature. In Figs. 2 and 3, our data are folded respectively with Hutchings' period (4.6117 days, Hutchings 1975) and the 5.7937days period of Aslanov & Barannikov (1989). Both periods can clearly be ruled out. Due to the severe aliasing of our time series, the 1.02day period taken from Vreux & Conti (1979) cannot be sampled over an entire cycle with our data. Though the scatter of the folded data (20 km s^-1 for $\Delta\phi\sim 0.1$ in 1987 and 10 km s^-1 for $\Delta\phi\sim 0.3$ in 1998) argues against this last period, it cannot be totally excluded. Meanwhile, we emphasize that no short period, typically from 1 to 5 days, appears in our data.

We have also applied the period research techniques to the He II EWs determined in those two runs. Again, no significant period appears. With the 1998 high-resolution data, we also searched for short-term variations in the line profiles: neither He I $\lambda$4471 nor He II $\lambda$4542 seem to change during the whole duration of our run. Short term variations of typically 1 to 5 days - if they exist - are thus only of very small amplitude.

Figure 2: RVs of He II $\lambda$4200 as measured on our 1987 spectra (open squares) and RVs of He II $\lambda$4542 from our 1998 data (filled triangles) folded with Hutchings' period of 4.6117 d and superimposed on his orbital solution.

Figure 3: Same as Fig. 2, but for the period of 5.7937 d proposed by Aslanov & Barannikov (1989).

4.2 Long-term behaviour

Since we do not detect any short-term variability in the He II RVs, we can average the He II absorption RVs for each observing run: we have plotted those means in Fig. 4, and we have combined these values with all published RVs in Fig. 5. We caution that the oldest data are rather uncertain, and that they should only be used for a qualitative analysis.

Figure 4: Mean RVs measured for each observing run: there are He II $\lambda \lambda$4200, 4542 absorptions (represented by filled triangles) and some emission lines like Si III $\lambda \lambda$4552, 4568 (stars), N III $\lambda \lambda$4634, 4641 (hexagons) and He II $\lambda$4686 (asterisks). The bottom axis yields the date in heliocentric julian days (HJD), while the x-axis on top of the panel indicates the year of observation: tickmarks represent the middle of the year quoted above. 1-$\sigma$ error bars are shown for He II $\lambda \lambda$4200, 4542 RVs (when no error estimates are shown, it means that only one spectrum was available).

The He II $\lambda \lambda$4200, 4542 lines are most probably formed in the deeper (photospheric) layers of the stellar atmosphere and can thus give rather unpolluted information about the star's actual motion. Other absorption lines (Mg II $\lambda$4481, Si IV $\lambda$4631 and all N III lines between 4510 and 4534 Å) and some emission lines (the unidentified Of emissions $\lambda \lambda$4486, 4504; Si III $\lambda \lambda$4552, 4568; N III $\lambda \lambda$4634, 4341; He II $\lambda$4686 and O II $\lambda$4705) display the same behaviour as the He II absorption lines. The RVs of some of these lines are shown in Fig. 4. On the other hand, the RVs of the main absorption components of H$\beta$, H$\gamma$ and He I $\lambda \lambda$4388, 4471, 4713 become less and less negative over the years of our observing campaign. This is linked to the long-term line profile variations discussed in Sect. 6.

The continuous trend of the absorption lines towards more negative RVs since 1922-1923, as reported by Underhill (1994), does not appear in our data. On the contrary, in 1994 and in 1996, the RV of He II $\lambda \lambda$4200, 4542 is about the same as in 1922. The absence of a clear very long term trend is best seen in Fig. 5.

Underhill (1994) also mentionned that the RVs of the absorption and emission lines show different behaviours. But in our data, He II absorptions and He  II, O  II, Si IV and N III emissions display quite similar behaviours (as can be seen in Fig. 4 and in Fig. 1 of Barannikov 1999). However, the "abrupt'' shift of the RVs towards more negative values in 1991, seen by Underhill (1994), does appear in our data as well as in those of Barannikov (1999). If intrinsic to a single star, this behaviour could indicate an episodic change of the velocity structure in the inner regions of the expanding atmosphere.

Using our data set only, a period of about 4600 days appears in the Fourier periodogram. However, with SL = 0.89, this detection is not significant. Moreover, this period completely disappears when we include the RVs determined by Plaskett (1924), Hutchings (1975), Vreux & Conti (1979), Underhill (1994) and Barannikov (1999). Considering the whole data set, no significant period becomes visible, the minimum SL reaching 0.93.

According to Barannikov (1999), the He II RVs should follow a period of 1627.6 d. But when we fold our data according to this period, it clearly appears that it is ruled out by our data (see Fig. 6). Barannikov used low-resolution photographic spectra, which are prone to errors (there are differences up to 70 kms^-1 between two consecutive nights for a 1627.6 days period with an amplitude K of only 10.5 kms^-1!): this might explain the important scatter seen in his orbital solution. We note that the minimum in Barannikov's radial velocity curve occurred in 1991, i.e. at the same epoch as we observe the RV shift discussed hereabove. However, our data do not suggest that this phenomenon is periodic.

Figure 5: All published radial velocities of absorption lines (mainly He II $\lambda$4200, 4542): the open squares represent the mean data from Plaskett (1924), the filled squares from Hutchings (1975), the open triangles from Vreux & Conti (1979), the stars from Underhill (1994) and the filled triangles from this work.