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Astron. Astrophys. 346, 487-490 (1999)

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3. Fourier parameters

As a further step, we fitted the V magnitudes by means of the formula


where f is the frequency, measured in cycles per day (cd-1 ). From the least-squares coefficients we calculated the Fourier parameters [FORMULA] (in particular [FORMULA]) and [FORMULA] (in particular [FORMULA]). These parameters are reported in Table 1; the mean magnitude of OGLEGC 29 is assumed from Kaluzny et al. (1996) as the values listed in the electronic table are shifted up by 2.5 mag. The period values obtained from the least-squares routine are listed, but they do not differ greatly from those reported by Kaluzny et al. (1996, 1997).


Table 1. The phases differences ([FORMULA]) and amplitude ratios ([FORMULA]) obtained from the Fourier decomposition are reported together with period values. The half-amplitude of the light variation is also reported. In 12 cases the [FORMULA] term (i.e. the first harmonic) was not detected.

Typical error bars are [FORMULA]0.33 rad for the [FORMULA] values and [FORMULA]0.05 for the [FORMULA] ones. Note that the amplitudes quoted hereinafter are those of the cosine terms, i.e. the half-amplitude of the light variation. No significant [FORMULA] term could be evidenced in 12 cases (OGLEGC 7, 24, 34, 35, 37, 40, 46, 59, 60, 63, 66, 70). For these stars the light curves do not deviate appreciably from a sinusoid: that means that if a 2nd-order fit is forced on the data, the error bar on the amplitude of the 2f term is larger than the amplitude itself. Following the same criterium, in 15 other cases the fit was stopped at the 2nd-order, in 6 cases at the 3rd and in two cases at the 4th.

Fig. 2 shows the [FORMULA] plot: the stars have been subdivided into three groups according to their amplitude and different symbols have been used. As can be noticed, there is a well defined trend in the diagrams. Moreover, the [FORMULA] values (open squares in Fig. 2) related to the galactic stars CY Aqr, ZZ Mic (Antonello et al. 1986) and V831 Tau (Musazzi et al. 1998) are in excellent agreement with those related to stars in [FORMULA] Cen.

[FIGURE] Fig. 2. The [FORMULA] [FORMULA] progression for short period stars in [FORMULA] Cen. Different symbols for different amplitudes: filled dots for [FORMULA] mag, open dots for [FORMULA] mag, crosses for [FORMULA] mag. The three open squares on the right side denote the three galactic stars CY Aqr, ZZ Mic and V831 Tau. Error bars are reported for the individual cases discussed in the text

There are some interesting cases:

OGLEGC 26 - The light curve is noisy (rms residual 0.033 mag), but its shape looks quite strange, with a descending branch steeper than the ascending one (Fig. 3, upper panel). The reality of the asymmetry is even more obvious when considering the mean light curve (Fig. 3, lower panel). In the Galaxy, there are two high-amplitude [FORMULA] Sct stars with a similar light curve: V1719 Cyg (Poretti & Antonello 1988) and V798 Cyg (Musazzi et al. 1998). Both these stars have a double-mode nature. Since the number of measurements of OGLEGC 26 is adequate (231 on 50 nights), a second period should be revealed by the frequency analysis, but we failed to find it.

[FIGURE] Fig. 3. The star OGLEC 26 shows an asymmetrical light curve, with a descending branch steeper than the ascending one (individual points, upper panel ). This asymmetry is even more obvious in the mean light curve (lower panel )

OGLEGC 29, 36, 39 and 62 - There are a few cases where the [FORMULA] values seem to deviate from the progression described by the others (Fig. 2). When considering the error bars, the [FORMULA] values of the light curves of OGLEGC 29 and 39 (3.72[FORMULA]0.66 rad and 4.02[FORMULA]0.82 rad, respectively) are only marginally deviating; in the case of OGLEGC 62 ([FORMULA] =4.13[FORMULA]0.56 rad) the line is just within the error bar of the related point. This discrepancy can be explained by observational scatter, since the amplitude of the [FORMULA] terms is very small. Moreover, the error bars may be optimistic since they are obtained from the formal error propagation. However, we note that the highest value (4.65[FORMULA]0.49 rad for OGLEGC 36) is the more reliable one and is farther than 3[FORMULA] from the others.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999