Astron. Astrophys. 356, 895-902 (2000)

3. Period analyses

3.1. HD 220392

3.1.1. Geneva data

The block of 124 data for HD 220392 covers an interval of 464 days (Table 1). We used the frequency step of cpd () with the PERIOD98 software (Sperl 1998). After Fourier analysis of the visual magnitudes, m_V, the frequencies, amplitudes and phases were improved by a least squares fit that gave a main frequency around 4.679 cpd, the same one as previously reported by Lampens (1992). The standard deviation dropped by more than 28 % after prewhitening for this frequency. Since the theoretically expected noise level of 0.006 mag for a bright constant star observed in the Geneva Photometric System (Rufener 1988) was not yet reached, a search for a second frequency in the prewhitened data was performed, revealing either 5.520 or 6.520 cpd. The (1 day)^-1 ambiguity due to the spectral window in the search for the second frequency is obvious (called "leakage effect" in Bloomfield 1976, see Sect. 3.1.2 below). The second highest amplitude was found for a two-frequency fit with 5.520 cpd: results of the simultaneous fits are presented in Table 2 (b).

Table 2. Results of a two-frequency fit (a) for the Geneva U and B data (b) for the Geneva V data and (c) for all 396 data of HD 220392 (program PERIOD98)

After prewhitening for the frequencies 4.679 and 5.520 cpd, the residual standard deviation falls to 0.0085 mag, still larger than expected. However, there is very clear evidence from the plots of the phase diagrams that the 7 data points on JD 2448518 have a level that is about 0.01 mag off compared to the rest of the data. This accounts for an extra 0.001 mag residual dispersion. A last Fourier analysis was done, giving 4.32 cpd and a standard deviation of 0.0073 mag after a third prewhitening. Evidence for this frequency is small (Sect. 3.1.2). Similar results are found for the Geneva m_U and m_B magnitudes. The fitted amplitudes for a two-frequency fit (preference was given to 5.520 cpd) are also listed in Table 2 (a).

3.1.2. ESO and Geneva data

Fig. 1. Amplitude spectra for the September 91/October 92 data. Notice the strong leakage effect that produces the 5.38, 6.38 and 6.52 cpd frequencies on both real and synthetic data

The combination of data was done in the V filter only, as the signal-to-noise ratio of the ESO B data is not as good as that of the V data and because there are fewer ESO U data. To this effect we adjusted for both stars the mean V values of the ESO (differential) data to the corresponding mean Geneva V magnitudes of the September 91 set. Thus adding the ESO data taken in October 1992 to the Geneva observations, a total of 396 V data with a time base of 866 days is available. We have tried different combinations with the datasets that confirm the results obtained with the Geneva data (Table 3). The number of nights (Nights) and the resolution per dataset (Resol.) are given as well. After prewhitening for 4.67 cpd, a new spectral analysis gives peaks at 6.52 or 6.38 cpd for all datasets, except for the complete set of 21 nights which gives 5.52 cpd. These frequencies are shown in brackets on Table 3. Among them, we have preferred 5.52 cpd for three reasons. First, it is the second dominant frequency in the largest dataset. Second, amplitudes for given by the least squares fit are always larger with 5.52 than with 6.52 cpd while standard deviations of the residuals are generally smaller after prewhitening with 5.52 cpd than in the case with 6.52 cpd. Third, an analysis made with the synthetic wave using the time window of September 1991/October 1992 gives as main frequencies 4.664 and 6.52 cpd, occulting the one of 5.52 cpd. This phenomenon is illustrated by Fig. 1 and is due to the "leakage effect" induced by the night/day alternation. Using these same arguments, we found that the frequency of 6.38 cpd as observed with the October and September/October datasets is also due to leakage, caused by a gap in the October 1992 campaign.

Table 3. Results of successive frequency analyses for HD 220392 (program PERIOD98).

On Fig. 1, there is an additional peak at 9.37 cpd but a least squares fit gives 4.32 cpd as a result for all datasets. However, evidence for this frequency is small as slight changes in the datasets do not confirm its existence: e.g. if we remove the data of only one night of Geneva photometry (JD 8518) this peak disappears. The frequencies for a double-frequency fit were determined by minimization of a subset of 321 data with no quality degradation (i.e. we removed the data of JD 8518 and the high-airmass data obtained at ESO). The results of the final fit for all 396 data are found in Table 2 (c). The best match is obtained with the set of frequencies (4.67439,5.52234). We present both mean light curves in Figs. 2 and 3: the first one shows all the data plotted against a frequency of 4.67439 cpd after having taken the 5.52 cpd variation into account while the latter one shows the same but this time against a frequency of 5.52234 cpd. The dispersion around both light curves is fair as it amounts to respectively 0.009 and 0.006 mag. Some 60 % of the initial standard deviation is thus removed.

Fig. 2. Phase diagram for the HD 220392-data against the frequency of 4.67439 cpd (after removal for the 5.52 cpd variation). Filled symbols represent the data on JD 2448518

Fig. 3. Phase diagram for the HD 220392-data against the frequency of 5.52234 cpd (after removal for the 4.67 cpd variation). Filled symbols represent the data on JD 2448518

3.1.3. HIPPARCOS data

The Hipparcos Epoch Photometry Catalogue contains 183 measurements of HD 220392 (HIP 115510). The note in the Main Catalogue however mentions that the "data are inadequate for confirmation of the period from Ref. 94.191" (ESA 1997). The reason is that all the quality flags are equal to or larger than 16, meaning "possibly interfering object in either field of view". The effective width of the aperture (called Instantaneous-Field-of-View ) is 38 arcsec, so companions at angular separations between 10 and 30 arcsec may interfere significantly during the measurement. We selected 177 data with a value of the quality flag not worse than 18, with a transit error on the (dc) magnitude not larger than 0.015 mag (2 data have not) and with good agreement between the (ac) and the (dc) magnitudes (1 datum has not) (ESA 1997, Vol. 1, Appendix A). In addition, we had to eliminate one more datum, the brightest one. The mean of the remaining data is 6.204 mag with a standard deviation of 0.024 mag. Fourier analysis between 0. and 23. cpd shows a peak at 4.6743 0.0001 cpd, i.e. the same main frequency as found in all former datasets. The corresponding phase diagram is illustrated in Fig. 4: the amplitude associated with is 0.013 mag large. The second frequency (5.52 or 6.52 cpd) is below detection: prewhitening for the main frequency still leaves a (large) dispersion of 0.021 mag. A double-frequency simultaneous fit attributes an amplitude of 0.013 mag to but only 0.003 mag to .

Fig. 4. Phase diagram for the HIP 115510-data against the frequency f1 (4.67439 cpd)

3.2. HD 220391

3.2.1. ESO and Geneva data

245 observations were obtained during the last two seasons only, spanning 14 nights. Again the data obtained on JD 8518 are conspicuously "low": the same effect as in the former data analysis was detected, implying an artificial increase in standard deviation of about 0.001 mag. We note the much smaller standard deviation of 0.0061 mag in the rest of the measurements. A frequency search was performed in a similar way as for HD 220392: only one peak at the frequency 0.42 cpd was found. However, the associated amplitude is below the expected noise level and the reduction of the standard deviation is very low (Table 4). Additional observation campaigns should be undertaken to investigate the reality of this frequency.

Table 4. Results of the single-frequency fit for HD 220391 (program PERIOD98)

3.2.2. HIPPARCOS data

The Hipparcos Epoch Photometry Catalogue contains 182 measurements of HD 220391 (HIP 115506). As in the first case, all quality flags are equal to or larger than 16. We selected 172 data with a value of the quality flag not worse than 18, with a transit error on the (dc) magnitude not larger than 0.020 mag (6 data have not) and with good agreement between the (ac) and the (dc) magnitudes (3 data have not). The mean of these is 7.227 mag with a standard deviation equal to 0.026 mag. Fourier analysis between 0. and 23. cpd displays a peak at 11 cpd (with an associated amplitude of 0.013 mag!), an artefact frequency of order , introduced by the rotation period of the satellite and very conspicuous in the spectral window Fouriergrams.

© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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