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Astron. Astrophys. 352, 239-247 (1999)

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3. Results

3.1. The humps: a distinctive character of the light curve

The differential light curves shown in Fig. 2 indicate the presence of prominent humps on March 1991 and 1995. The humps are roughly symmetrical lasting by about 65 minutes and followed by a slow magnitude decrease (March 1991) or by a secondary low-amplitude hump (March 1995). This picture sharply contrasts with that observed on early 1998 (Fig. 3). The humps are completely absent on January-February 1998 and re-appear (with secondary humps) on March 1998 and January 1999 (Fig. 4). A remarkable feature is the absorption like feature seen on January 1998. We will show in the next section that this feature is the "embrion" of the fully developed humps seen two months later.

[FIGURE] Fig. 2. Differential magnitudes on March 1991 and 1995. Note the high amplitude humps. A typical error is shown by the bar in the upper right corner of every panel.

[FIGURE] Fig. 3. Differential magnitudes at early 1998. Note the absence of humps in the upper panels and the different vertical scale in the panels. A typical error is shown by the bar in the upper right corner of every panel.

[FIGURE] Fig. 4. Differential magnitudes on January 1999. The humps appear again. A typical error is shown by the bar in the upper right corner. The double arrow shows the length of the photometric period.

3.2. The long-term light curve

Fig. 5 shows the long-term light curve of RZ Leo during 1987-1999. It is evident that the quiescence mean magnitude changes by several tenths of magnitude in a few years and at 3.5 [FORMULA] 10-3 mag d-1 during January and March 1998. Unfortunately, the faintness of the object has prevented a continuous monitoring, so the long-term data are inevitably undersampled.

[FIGURE] Fig. 5. Mean magnitudes of RZ Leo during 1987-1999. Error bars indicate nightly rms. Data are from Howell & Szkody (1988, open circles), Mennickent (in preparation, crosses) and this paper (solid circles).

3.3. Searching for a photometric period

We removed the long-term fluctuations normalizing the magnitudes to a common nightly mean. Then we applied the Scargle (1982) algorithm, implemented in the MIDAS TSA package, which obeys an exponential probability distribution and is especially useful for smooth oscillations. In this statistics, the false alarm probability [FORMULA] depends on the periodogram's power level [FORMULA] through [FORMULA], for small [FORMULA], where N is the number of frequencies searched for the maximum power (Scargle 1982, Eq. 19). In our search we used N = 20000, so the 99% confidence level (i.e. those corresponding to [FORMULA] = 0.01) corresponds to a power [FORMULA] = 14.5. The range of frequency scanned was between the Nyquist frequency, i.e. 1.7 [FORMULA] c/d and 1 c/d. After applying the method to the whole dataset many significant aliases appeared around a period [FORMULA]. Apparently, the light curve was characterized by a non-coherent or non-periodic oscillation. We decided to start with our more restricted dataset of March 1991. The corresponding periodogram, shown in Fig. 6, shows a strong period at [FORMULA] (108.9 [FORMULA] 1.7 m, the error correspond to the half width at half maximum of the periodogram's peak) flanked by the [FORMULA] 1 c d-1 aliases at [FORMULA] (the period found by Howell & Szkody 1988) and [FORMULA]. The ephemeris for the time of hump maximum is:


[FIGURE] Fig. 6. The Scargle periodogram for the magnitudes of March 1991. The central peak at [FORMULA] is flanked by the [FORMULA] 1 c d-1 aliases at [FORMULA] and [FORMULA]. The dot-dashed line indicates the 99% confidence level.

In order to search for possible period changes we constructed a [FORMULA] diagram based on timings obtained measuring the hump maxima. These timings, given in Table 2, were compared with a test period of [FORMULA]. The [FORMULA] differences versus the cycle number are shown in Fig. 7. Apparently, the period is not changing in a smooth and predictable way. In principle, the [FORMULA] differences are compatible with non-coherent humps and/or period jumps. To explore both possibilities, we searched for seasonal periods. Only datasets of March 1991, 1995 and 1998 were dense enough to construct periodograms. The results, given in Table 3, suggest a non-coherent signal rather than a variable period. In summary, the data are compatible with humps repeating with a period of [FORMULA] but in a non-coherent way. Armed with a photometric period, we constructed seasonal mean light curves. Only nights with fully developed humps were included. The results, shown in Fig. 8, clearly show secondary humps around photometric phase 0.5. These mean light curves are provided as a hint for future light curve modeling.


Table 2. Times of hump's maximum. HJD' means HJD - 244 0000. Measures are from our light curves shown in Figs. 2 to 4 except those indicated by [FORMULA] (derived from the Howell & Szkody's 1988 light curve) and [FORMULA] (Mennickent, in preparation).

[FIGURE] Fig. 7. O - C diagram for the times of hump maximum, with respect to a test period of [FORMULA]. Data are from Table 2. In principle, the figure is compatible with a non-coherent signal or with period jumps at some epochs.


Table 3. The hump period at different epochs. Our results are consistent with a single period.

[FIGURE] Fig. 8. Mean light curves of fully developed humps, shifted to a common phase of maximum. The curves are normalized to zero mean intensity.

3.4. "Anti-humps" and long-term hump evolution

A review of the observations of early 1998 including the discovery of "anti-humps" was given by Mennickent & Sterken (1999). Here we present a more complete analysis of the phenomenon. Fig. 9 shows in detail the events of early 1998. The light curves have been binned with a period [FORMULA], accordingly to Table 3. The evolution of the hump is singular. It starts as a [FORMULA] absorption feature (07/01/98) then disappear from the light curve (11/01/98 and 06/02/98) and then re-appears like a small wave (07/02/98) and fully developed symmetrical hump (18/03/98 and 19/03/98). Secondary humps are also visible, with amplitude roughly 60% the main hump amplitude. On February 7 a secondary absorption hump is also visible, along with the main absorption feature. These "anti-humps" appear at the same phases where normal humps develop a month later. A close inspection to the data of February 7 reveals another alternative interpretation: the observed minima could define the base of the humps. We have rejected this hypothesis for three reasons: (1) it does not fit the ephemeris, indicating a possible shift of the hump maximum by about 0.2 cycles, (2) the peak-to-peak distance between main and secondary maxima should be 0.3 cycles instead 0.5 cycles, which is observed the other 3 nights and (3) the secondary maximum should be about 80% of the main peak, contrasting with a value of 60% observed other nights. We provide an interpretation for this phenomenon in the next section.

[FIGURE] Fig. 9. Light curves of RZ Leo during early 1998 folded with a period [FORMULA].

Fig. 10 shows the hump's amplitude roughly anticorrelated with the nightly mean magnitude, as occurs in VW Hyi (Warner 1975). As shown in Fig. 9, this anti-correlation is not only due to the increase of hump brightness, but is also a true rise of the total systemic luminosity, through the whole orbital cycle. The outlier in Fig. 10 is a measure by Howell & Szkody (1988) which is a rather doubtful point. In fact, accordingly to these authors, since their primary goal was to obtain differential photometry - not absolute photometry - they calibrated their magnitudes using only a few standards per night. They give a formal error of [FORMULA] for the zero point of RZ Leo, but with so few standards observed, not in the same CCD field, it is difficult to control systematic errors due to variable seeing and atmospheric transparency. In the following, we will omit this outlier from our discussion. Returning to Fig. 10, we observe that the hump disappears when [FORMULA] and attains maximum amplitude when [FORMULA]. Surprisingly, the hump becomes "negative" (i.e. an absorption feature) when the system drops below [FORMULA] 19 mag. A linear least squares fit to the hump amplitude [FORMULA] yields:


where V refers to the nightly mean V magnitude.

[FIGURE] Fig. 10. Hump amplitude versus nightly mean magnitude and the best least-squares linear fit. The outlier by Howell & Szkody (1988, open circle) is discussed in the text.

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© European Southern Observatory (ESO) 1999

Online publication: November 23, 1999