Astron. Astrophys. 327, 231-239 (1997)

4. Orbital variations

The lightcurves are obviously disturbed by strong flickering with amplitudes up to 0.7 mag, consistent with the values given by Bruch (1992). However, they also show variations on timescales much longer than usually conceded to flickering. To search for periodicities, we therefore applied the AOV algorithm to the normalized photometric data (normalization has been performed by substracting mean values from the individual lightcurves).

The resulting periodogram is shown in Fig. 5. It shows a peak around the orbital period which, however, is by far not the strongest one.

Fig. 5. The resulting periodogram of the AOV analysis of the photometric data. The arrow indicates the orbital period

When folded with the orbital period, the photometry reveals two periodic features, a big hump with a width of 0.25 orbital phases and an 0.15 phases wide small hump (Fig. 6). The distance between the maxima of the big and the small hump, resp., is 0.45 phases, i.e. they are not exactly at opposite phases. When compared to the zero points derived by the spectroscopy, these maxima are at phases 0.33 (big hump) and 0.78 (small hump) for , and at phases 0.58 and 0.03 for .

Fig. 6. Lightcurves of WW Cet. a The individual lightcurves, derived from the photometric data in Fig. 1. Data are folded on the periods (top) and (bottom) taking the zero points from the spectroscopic data. Magnitudes have been normalized by substracting the mean value for the respective nights. Two orbits have been plotted for clarity. b Mean lightcurve for period . The mean value of all datapoints within an interval of 0.05 orbital phases has been calculated. Again, two orbits are shown

The phenomenon of a main and an intermediate hump is visible in the lightcurves of several CVs and is usually explained with a hot spot visible both from front and back (e.g. Schoembs & Hartmann 1983). These humps are normally more extended than the features in our photometry, but here their structure is severely disturbed by the present strong flickering which is of comparable amplitude. However, both of our possible periods give very unusual phasings as the maximum of the main hump is usually seen just before a photometric eclipse, i.e. around phase 0.9.

On the other hand, the spectroscopic data in quiescence give evidence for an unusually located H emission region (Tappert et al. 1997). In Fig. 7 we show the 1993 data binned into corresponding phase bins. An S-wave with zero points around phases 0.4 and 0.8 is clearly visible. Applying a function of the type in Eq. (2) to the maxima of the spectra yields km/s, km/s, and , i.e. phases 0.13 (superior conjunction) and 0.63 (inferior conjunction). The phases of the maxima of the radial-velocity curve - which correspond to maximum visibility of the source and therefore to possible maxima in the lightcurve - are thus 0.38 and 0.88. Although not being identical, this points in the direction of the phases of the humps with respect to . This might also be another indication that this is the more probable period.

Fig. 7. The 1993 spectroscopic data binned into corresponding phase bins. The data have been corrected for orbital variations with respect to (there are practically no differences when applying ), and they have been smoothed for clarity. The numbers at the right border of the plot give the number of spectra per bin. Phase bin 0.0 is identical to phase bin 1.0.

We also compared the phases of the humps with the published photometries of Paczyski (1963) and Hollander et al. (1993, hereafter HKP93). The values of the corresponding HJDs are given in Table 6. However, when comparing them to Figs. 1 and 9 of Paczyski and HKP93, respectively, no clear evidence for similar features around these times can be found. Possible reasons are the following:

Table 6. Comparison of the phases of the big hump (bh) and the small hump (sh) to the photometries of Paczyski (1963) and Hollander et al. (1993). Given are the HJDs which correspond to the maxima of the humps.

1. a) Our ephemerides are wrong. Although we applied great care when determining them, this is a possibility which cannot be excluded. On the other hand, a time-series analysis of the HKP93 data does not show any indications of the orbital period (Fig. 8), and it is therefore more probable that the humps are not present in their data.
2. b) The features in our lightcurve are caused by aperiodic variations which just appear to be similar structures at similar phases. This does not sound very convincing either, because our data covers the phases of both humps fully or at least partly for every night.
3. c) The humps are a temporary phenomenon which appeared only recently (i.e. during the last 7 years) or shows up only at certain brightness levels. Paczyski's data shows the system at 13.8 mag, i.e. 0.4 mag brighter than during our observations, while the values given by HKP93 are around 15.0 mag and thus 0.8 mag fainter. Thus Paczyski's data represent quite well the mean quiescence value, while our data lie towards the lower end of the distribution, and HKP93 caught the system at a very rare low brightness (Fig.3 of R96). A with varying brightness disappearing and reappearing intermediate hump has been observed e.g. in VW Hyi (Vogt 1974), and disappearing main humps have been reported for nova-like variables (e.g. Schlegel et al. 1983 for UX UMa in an 0.25 mag brighter state than normal), but to our knowledge there has been no system observed where both humps would disappear.

Convinced of the reality of the humps and their phasing, we are still left with the problem that we find two humps in the lightcurve (with the main one being at superior conjunction) but apparently only one S-wave source. One possibility is that there are two impact regions from the gas stream from the secondary, one at the close and the other at the far side of the disk (seen from the secondary). The H emission from the first impact region must then be suppressed somehow, possibly hidden by the optically thick stream, as was suggested for RX And by Kaitchuck et al. (1988).

Fig. 8. Time-series analysis of the data of HKP93. The arrow indicates the orbital period

The other possibility is that the stream is spilling over the disk without impacting at the close side (or at least not strong enough to produce H emission or a photometric hump) producing only one hot spot at the far side of the disk which is then seen both at superior and inferior conjunction. However, for our parameters, the calculations by Lubow (1989) yield an impact site in the inner disk at 0.4 - 0.5 ( is the disk radius). This corresponds to a much higher velocity than observed (note that the distortion is near the center of the line, i.e. originates from low-velocity material). Another drawback of this scenario is that it fails to explain the phase difference between both humps which departs slightly but significantly from 0.5.

Unfortunately, the S/N of our data is not high enough to really resolve and extract the S-wave contribution. We therefore highly recommend further observations with similar (or better) spectral resolution on bigger telescopes.

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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