Astron. Astrophys. 338, 465-478 (1998)

3. Optical variability

3.1. Long term variability

During the observed time span RX J0203 was found to display changes of the overall brightness level, as it is demonstrated in Fig. 2, where all available V-band magnitudes are compiled. For most occasions (1992, 1993, Dec. 1996 and 1997) the system was in a high state with a mean brightness V reaching . It's magnitude was significantly lower by about 1 mag during the intermediate state observed between Oct. 1995 and Feb. 1996, whereas for the single observed low state observation (Sep. 1994) it dropped to .

Fig. 2. Long term V-band light curve of RX J0203 . The vertical bars indicate the orbital variability for each observation.

A representative set of orbital V-band light curves corresponding to the different brightness levels described above is displayed in Fig. 3. The original data were folded over the photometric ephemeris derived below. The most obvious feature of the high states observed in 1993, 1996 and 1997 is a quasi-sinusoidal variation with a period of 4.6 hours. The full range of the orbital variation is 0.7 - 0.9 mag. A similar light curve pattern was observed in the intermediate brightness state Oct. 1995 - Feb. 1996. We refer to this brightness variation as regular mode.

Fig. 3. V band light curves as a function of the photometric phase. Some data were plotted twice for clarity (open circles). Typical photometric errors are 0.05 mag.

It is in drastic contrast to the light curve pattern observed in another high state in Oct. - Nov. 1992 (Fig. 4). The V-band light curve of Oct. 29, 1992 appeared asymmetric with a steep rise and a shallow decline. The orbital minimum was shifted to a later phase, , with respect to the finally accepted photometric ephemeris of that feature. The R-band light curves of Nov. 24 - 27, 1992 were double humped with the main minimum at being very sharp. These changes are most likely explained by changes of the shape, the size and(or) the location of the accretion region. We refer to this brightness variation as irregular mode.

Fig. 4. Differential RV band light curves obtained in October/November 1992 as a function of the photometric phase. Some data were plotted twice for clarity (open circles). The light curves are shifted by 0, 1.25, and 2.5 mag, respectively.

The low state light curve (Fig. 3, lower curve) is almost flat with strong flares ( mag) superimposed. Any remaining orbital variation was lower than 0.25 mag.

3.2. The photometric period

The stable photometric pattern found in the 1993 and 1995-1997 light curves enabled us to establish a common photometric period. All data except those obtained in the low state or in the irregular mode of accretion entered our period search. We used two different approches for the period analysis. The first is a simple least-squares method (see Schwope et al. 1991) applied to the heliocentric timings of all observed minima. These were estimated by fitting gaussians to the light curves and are listed in Table 2. The quantity which determines the significance of a period is the inverted squared sum of the values (observed minus calculated). This was computed from the phasing of the minima for each trial period. The second is the so-called analysis-of-variance (AoV) method (Schwarzenberg-Cerny 1989) which is appropriate for non-uniformly distributed observations and makes use of every single data-point by folding and binning with a trial period.

Table 2. Heliocentric timings of the photometric minima a) Errors resulting from gaussian fit

Both methods yield consistently a most probable period of (Fig. 5a-c). All other periods, in particular the one-day alias period at 3.8 hours, can be ruled out. The occurrence of alias periods in Fig. 5a-c is caused by the typical sampling length of 1 year. The least-squares method (panel a) is more robust than the AoV method (panel b) in discerning the true period from the alias periods. A weighted linear regression of all V-band minima yields the photometric ephemeris,

where the numbers in brackets represent the uncertainties in the last digits. The residuals of the linear fit (observed minus calculated times of the photometric minima) are shown in Fig. 6. Although for the period determination only the minima in the V-band were used, minima observed in other wavelength bands were included in the figure. (Quasi-)simultaneous multicolour-photometry reveals clearly that the orbital minimum occurs dependent on colour. This is nicely illustrated by the light curves obtained in September/October 1993 (Fig. 7). The I-band minimum lags the B-band minimum by 0.12 phase units.

Fig. 5. Periodograms derived from optical photometry (panel a and b ) and the radial velocity variation (panel c ). The photometric period was estimated using our least-squares method applied to the minima given in Table 2 (panel a) and the analysis-of-variance method (Schwarzenberg-Cerny 1989) for the data from 1993-1997 (panel b ). The lower panel c shows the analysis-of-variance statistic for the combined high and low resolution spectroscopy radial-velocity data. Likely periods appear as maxima. The most probable period of 16566.7 sec (4.6 h) is consistent with all the data.

Fig. 6. Diagram of observed minus calculated times of photometric minima computed with respect to the linear ephemeris of Eq. 1. Filters used for some observations are indicated.

Fig. 7. Differential light curves obtained in September/October 1993 showing quasi-periodic oscillations plotted as a function of the photometric phase. Some data were plotted twice for clarity (open circles). The light curves are shifted by 0, 1, 2, and 3 mag respectively.

Apart from the colour-dependence of the minima there is some remaining phase jitter in the V and R band minima in excess of the formal errors. The latter might be underestimated regarding the variable shape of the individual light curve minima.

The absence of a flat-bottomed part of the optical light curves in the regular mode of accretion and their close resemblance to other polars like e.g. MR Ser (Schwope et al. 1991) suggest that the light curves are modulated by cyclotron beaming. With that type of light curve the accretion region is continously in view and in particular undergoes no selfeclipse by the white dwarf. The colour-dependent minima may probably be explained by optical depth effects in a structured accretion region.

3.3. Optical quasi-periodic oscillations (QPOs)

Several of our light curves obtained during the 1993 high state display rapid QPO-type variations (Fig. 7). All observations obtained in August and September display this behaviour. The QPO variability is dependent in strength on phase and photometric bandpass. They were generally strongest around phase and in the U-band (0.4 mag peak-to-peak), and generally weakest around phase and in the I-band. From Fourier analysis we found two distinctive types of QPO-periodicities, one group occurs at  min, a second group has  min.

Low frequency oscillations in AM Herculis objects are reported for half a dozen systems both at X-ray and optical wavelengths (Chanmugam 1995). A model to explain these was proposed by King (1989) and involves oscillations of the ionization front near the -point. The periodicities predicted by this model are 0.055 equivalent to 13.7 min for RX J0203. Our measurement of 14 min is in good agreement with that prediction. We note that RX J0203 occasionally displays QPOs at half that period which might represent the first harmonic. A similar behaviour, QPO-type variations at two periodicities being multiples of each other, has been found in AM Her, VV Pup (Schaefer et al. 1994) and V1309 Ori (Shafter et al. 1995), but RX J0203 is the only system showing both periodicities simultaneously.

© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998
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