Astron. Astrophys. 343, 909-915 (1999)

5. Frequency analysis of the data set

Nightly light curves obtained during outburst maximum and decline show light variations with typical amplitude , or slightly less. They also contain random flickering and quasi-periodic oscillations with typical timescales of tens of minutes, as well as the slower (hours) variations.

The original light curves for every night are given in Fig. 3. We analyzed the brightness changes with the Irregularly Spaced Data Analysis (ISDA) package (Pelt 1980, 1992). Prior to period search, we subtracted from the data a trend corresponding to the smoothed shape of the outburst.

Fig. 3. Original light curves in B, obtained in June-October 1997. The abscissa is given in truncated Julian date.

5.1. Hourly variations

At first we analyzed the variability near the orbital period. Within ISDA we used different methods for different data sets: all data, and data only from the top of outburst. We found that the periodogram computed for the latter data set shows a better signal-to-noise ratio than those for all the data. In Fig. 4 the periodogram for these "top" data in the frequency range of 1-50 cycles/day is given. It is computed by the Stellingwerf method with the Abbe statistic, also known as the Lafler-Kinman statistic (Lafler & Kinman 1965). There the value of the statistic is less then 1 for trial periods close to the real one, and is close to 1 at other frequencies. In our analysis we give twice the value of the Abbe statistic.

Fig. 4. The periodogram for MV Lyr (June data set) computed by Stellingwerf method in the region of 1-50 cycle/day. The two peaks closest to the position of the orbital period are marked by arrows.

There is a wide and double peak in the periodogram, centered on the 7.52 cycle/day orbital period. Surrounding this peak are components with 1-day aliasing. The data folded on the periods, corresponding to the two components close to the orbital period (0.1294 and 0.1487 d) give much smaller error then these on the periods of the remaining peaks. Because they are aliased, we cannot choose between them immediately.

5.2. Choice of likely period

Let's compare the closest period to the orbital one from different points of view.

The data folded on these two periods are shown in Fig. 5. They are binned into 20 intervals, and the standard deviation is marked by the vertical bars, which include the intrinsic variations - flickering and QPOs. The light curves are constructed for the same zero-epoch: . Both light curves have an amplitude about and an asymmetric shape.

Fig. 5. Data folded on two trial periods: 0.1294 d (upper panel ) and 0.1487 d (lower panel ).

If the real period is 0.1487 d, it could be interpreted as the period of a positive superhump (), because it exceeds the orbital period (). We then could examine the position of MV Lyr in the known empirical relation between the fractional period excess and orbital period (Stolz & Schoembs 1981, 1984) for the known superhumpers with apsidal disk precession (Vogt 1982; Whitehurst 1988; Lubow 1991). This relation is shown in the upper panel of Fig. 6 for all superhumpers as of mid-1998 (Patterson 1998). The 2nd order polynomial fit is shown by line. MV Lyr in the last high state as well as the old nova V603 Aql are placed far below the relation, while MV Lyr in the present outburst is far above it.

Fig. 6. The relation between fractional period exess and orbital period for both positive (open circles in upper panel) and negative (filled circles in lower panel) superhumpers. The deviated data of V603 Aql and MV Lyr in a high brightness state are marked by triengles. The present for two suspected periods of MV Lyr are marked by square.

The deviations of MV Lyr positions in both brightness states significantly exeed a scattering of the rest points over the line and fairly differ from each other. It is known that superhumps periods decrease from the time when they were first detected. However the differences in the MV Lyr deviations are too large to be explained as possible change in the superhump period: The differences between extremal values of superhump periods, normalized to the orbital periods, don't exeed 1,5 per cent for different superhumpers (see, for example, Patterson et al. 1993a, Leibowitz et al. 1994, Patterson et al. 1997).

The period of 0.1487 d implies that the period of apsidal precession d according to the relation

From another relation (Osaki 1985) we can estimate the accretion disk radius:

where q is the mass ratio of the secondary () to the primary (). Taking (Skillman et al. 1995) or more relevant for the case of tidal instability, 0.3, we obtain . This is comparable or slightly larger then the primary's Roche Lobe, namely (Pringle & Wade 1985), where a is the binary separation.

On the other hand, a period of 0.1294 d might be interpreted as a negative superhump period as it is less than P_orb. Recently it has become known that a few cataclysmic variables display superhumps with negative period excess (Patterson et al. 1993b).

In this case . This value is close to that for known negative superhumpers: the novalike TT Ari shows (Thorstensen et al. 1985, Udalski 1988), while the old nova V603 Aql shows -0.029 (Patterson et al. 1997), and the SU UMa-type binary V503 Cyg shows -0.025 (Harvey et al. 1995). The position of MV Lyr within the negative superhumpers is given in a lower panel of Fig. 6.

So the arguments considered above indicate that is preffered over .

5.3. Short-term light variations

The second point is flickering and short-term light variations. In order to investigate them, we subtracted from the individual-night data the best fits with period 0.1294 d and calculated the power spectra for every nightly data set, using a standard (Deeming 1975) Fourier transform analysis.

Then we selected five power spectra for the longest observational runs showing the short-term light variations with highest amplitude. The average of these power spectra is shown in Fig. 7a. The dip at low frequencies is caused by the subtraction of the best fit trend. The continuum is well fit to the function S(f) in the shot noise model (Panek 1980):

where S is the power and f is the frequency, measured in c/day. In this model the flickering is described as the overlapping of a series of randomly occuring flares (shots) of well-defined shape. We found the e-folding time (decay time) of the flares to be 242 s.

Fig. 7. a The mean power spectrum for the 5 selected nights. The region of a shot-noise model (in accordance with Eq. (3)) is shown by the lines. b  Fourier periodograms for the all data. c  Periodogram computed by the Stellingwerf method.

Andronov (1996), using two short data sets of a single night, obtained decay times of 41 and 64 s for the high brightness state. Decay times determined for other CVs are 41-73 s for AM Her (Panek 1980); 160 s (Silber et al. 1997) and 92 s (Andronov, 1996) for BY Cam. All these are much shorter than we found for MV Lyr.

There are several broad peaks in the power spectrum which exceed the limits of the shot-noise model. They correspond to periods of 19.2 min (most significant peak), 29 min, and 47 min (less significant peaks). We could see that these periods exist at least within months, but their phases are wandering and they are rather quasi-periods, not strong periods: If we calculate the periodogram for all data (which span about 4 months) with fixed zero epoch, these periods do not disappear, but their significanse decreases. This is demonstrated by the Fourier periodogram (Fig. 7b) and more clearly - the periodogram computed by the Stellingwerf method (Fig. 7c). Comparison with the mean power spectrum reveals that the period of 19.2 min is the most stable.

The mean light curve of the data, folded on this quasi-period, is shown in Fig. 8. Its amplitude is . In constructing this light curve, we included all data from the June-October data set, even those which did not show the high-amplitude fast variations.

Fig. 8. All data, folded on the 19.2 min period and binned into 20 phase intervals.

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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