Astron. Astrophys. 354, L13-L16 (2000)

3. Data reduction and analysis

A first spectral analysis of the whole data set yielded no significant results at frequencies higher than 50 mHz. Then the data sets were rebinned at an effective resolution of 10 s and a definitive analysis was performed. The sky background has been removed by means of a linear interpolation between the mean values obtained at the beginning and at the end of each observational run performed around the meridian. We have calculated the magnitudes of the target and comparison stars taking into account the differential extinction. Times have been reduced to the solar system barycenter using the Stumpff (1980) algorithm. As output from the reduction process we obtain a file with the Julian date, the magnitudes of PG 0856+121 and of the comparison star, and the difference of magnitude between the two stars with their errors. Fig. 1 shows the light curve of PG 0856+121 obtained during the run of March 26, 1998, where the light variations are clearly visible.

Fig. 1. Light curve of PG 0856+121 during the run of 26th March 1998.

Fourier spectral analysis was performed by using Deeming (1975) method, modified by Kurtz (1985); the results were checked performing a second analysis with Period98 (Sperl 1998). The analysed frequency range spans from 0 to 50 mHz. The noise mean power was computed in the range 1-15 mHz by using Kepler (1993) formula. This produces an overestimation of the noise mean power (MP) as in this range there are the most prominent features of the power spectrum. Our criterion for acceptance states that a feature in the Fourier power spectrum is considered trueif greater than five times the mean power value. Taking into account the overestimation of the noise mean power, this criterion is even more restrictive.

Fig. 2 shows the power spectra of PG0856+121 (difference of magnitude) of the following runs: a 26th March 1998; b 27th March 1998; c sum of 26th and 27th March 1998. In the power spectra of March 26th two peaks are present at 2.3 and 3.2 mHz with a resolution of 0.2 mHz. Their values in power and the corresponding statistical significances are 3.0 mmag at 8 and 3.5 mmag at , respectively. The same periodicities, but with a lower resolution because of the shorter length of the run, have been found in the night of April 14, 1998. These frequencies are not evident in the two runs of December 1998. A thorough analysis of the contemporaneous observations performed on the comparison star and of all data collected in the frame of our observational campaign allows us to exclude any artifact corresponding to these pulsations; only one time we found a significant periodicity of 0.5 Hz, due both to a worn joint connecting the step motor to the right ascension gear box and to an incorrect positioning of the target star near the diaphragm border; also the CCD autoguide system, repeating the pointing corrections with a period of about 15 s, cannot introduce such a so low frequency characteristics in the power spectrum; therefore, considering these frequencies as real, foldings of rebinned data modulo 2.292 and 3.171 mHz respectively have been constructed with pre-whitening by the other period and without. The results were non significantly different, so non pre-whitened foldings have been preferred (although more noisy) because obtained directly from data without any mathematical handling. They have been reported in Fig. 3. Each dot represents the mean of all measurements included inside a 0.05 phase interval and it corresponds to about 270 original measure points performed with 1 s sampling time.

Fig. 2a-c. Power spectra of the difference of magnitude of the two stars: a the run of 26th March 1998; b the run of 27th March 1998; c sum of the runs of 26th and 27th March 1998.

Fig. 3a and b. Foldings of PG 0856+121 data in the night 26th March 1998, performed without any pre-whitening: a modulo 436.30 s; b modulo 315.36 s. Each point of the two graphs represents the mean value obtained inside a 0.05 phase interval and is obtained from about 270 1s samples

© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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