Astron. Astrophys. 359, 1068-1074 (2000)

4. PG 1618+563: photometry

PG 1618 was observed at the 2.5 m Nordic Optical Telescope (NOT) in two runs, July and October 1999 ¹, using respectively the Tromso-Texas 3-channel photoelectric photometer with Hamamatsu R647 photomultipliers (PMTs), and the High Resolution Adaptive Camera (HiRAC) with Loral Lesser thinned 20482048 CCD chip, modified with our own control software to be able to run in high-speed multi-windowing mode.

4.1. Calibrations

In both runs we measured the magnitude of PG 1618, which are reported in Table 1; they are in agreement with the Strömgren b magnitude of 12.7 measured by Wesemael et al. (1992) for both stars together. The uncertainties are quite high because of the small number of Landolt standards used (3 with different colours in July, just one in October); moreover, the small separation between the two stars rendered the calibration of the single components more difficult.

4.2. Time-series: observations and data reductions

Table 2 contains all the information relative to the time-series observations. In the first run of July 1999 we used only 2 channels (target + sky) of the photoelectric photometer because of some focusing problems with the telescope. Nevertheless, the lack of comparison star did not significantly affect the quality of the results thanks to the high stability of the sky. The presence of the F3 star at 3.7 arcsec in the S-W direction forced us to use medium size apertures (10.3 and 14.7 arcsec), in order to include both stars in the diaphragm. Some attempts to exclude the F3 star using a 5.1 arcsec aperture did not give good results. In the CCD observations of October 1999, the sky area available for a reference star was limited by the chip area to about 3.7x3.7 square arcmin. Hence in the U and B bands we were forced to use PG 1618A only as comparison star; nevertheless, the high space resolution of HiRAC (0.1 arcsec/pix) permitted us to separate the two objects and obtain good results even in this situation. In the R band a further reference star with a brightness comparable to that of the target was observed. Moreover, in all bands the sky was monitored in two independent fields on each side of the target, at a reasonable distance from it.

Table 2. Time-series Photometry

The data were reduced on line using the standard WET (Whole Earth Telescope, Nather et al. 1990) software for the PMT data and the Real Time Photometry (RTP, Ostensen & Solheim 2000) program for the CCD data, developed by one of us (R. Ostensen) as part of his Ph.D.-project. Then all the data were reduced again with a more accurate procedure including smoothing of the sky, compensation of long time-scale trends, extinction corrections; and also better flat fields, optimization of the aperture size, and MAP ² technique for the CCD data.

4.3. Amplitude spectrum

4.3.1. No-filter data

The light curve of July 20, which has the highest S/N ratio, shows a periodicity of about 140 s, with a 4300 s modulation (Fig. 3). The amplitude spectrum of the same observation presents a doublet of close frequencies at about 6.95 and 7.16 mHz (Fig. 4), which explains the modulation effect (P_beat P²/P 4800 s). The two frequencies are also visible in the observation of July 22 (Fig. 4); in July 21 only one peak appears, but both the data quality and the frequency resolution are lower in this observation.

Fig. 3. No-filter light curve of July 20. Two beat periods are clearly visible.

Fig. 4. Amplitude spectra of the no-filter data. The bottom plot shows the spectrum of the three consecutive nights together; the two smaller panels represent the same spectrum with a larger scale (left) and its spectral window (right).

In order to obtain more accurate frequencies, we have joined together the three consecutive observations and calculated the amplitude spectrum of the entire set (Fig. 4). Then we have applied a least-squares two-sinusoid fit to the data to optimize amplitudes and frequencies (and phases). The results are:

f₁=(6947.6 0.1 n11.6) µHz, a₁=(1.45 0.04) mma;

f₂=(7180.3 0.3 n11.6) µHz, a₂=(0.86 0.04) mma.

The first indetermination on the frequencies is the formal error of the fit, whereas the second one is due to the one-day aliases (11.6 µHz = 1 cycle/day) created by the lack of data between one night and another (see bottom panel of Fig. 4). The integer number n should not be larger than 2 or 3 in absolute value.

Looking at Fig. 4, the amplitudes of the two signals are different from one night to another; in the last night the ratio of the amplitudes is inverted respect to the first night. Because of the low frequency resolution, it is not clear whether the amplitudes variations are real or due to interference between unresolved close frequencies. For the same reason, to search for further small-amplitude signals can not produce definitive results. Nevertheless, in both the observations of July 20 and 22, one can note some power near 6.25 and 7.73 mHz, which is not due to windowing effects, as we checked subtracting the two main frequencies from the data.

To investigate this further, we have used the `Delta method', often used in the context of blazar variability (see Hagen-Thorn et al. 1997 and references therein). The Delta method is based on a `pre-whitening' technique i.e., after each subtraction of a sinusoidal component, periodograms of the residuals are constructed and analyzed again. Since white noise has a constant spectral density, the dispersion of the residual series decreases linearlywith increasing number n of subtracted harmonics:

where is a sinusoid of the form , N is the total number of points in the time-series and is the time-series itself.

Thus, in a sense, the very presence of noise establishes the optimum number of sinusoids required to characterize the maxima in the power spectrum. Having applied this method to our data results in Fig. 5, which shows the dependence of on the number of subtracted sinusoids. The figure shows that we cannot expect to fit more than 2 sinusoids (n=0 is a constant term) to the data, since we would be descending into white noise.

Fig. 5. Dependence of on the number of subtracted harmonics. n=0 refers to the subtraction of a constant term. The n=3 and n=4 sinusoids, fitted at 6937.7 and 7079.3 respectively, are not significant and merely serve to demonstrate the linear dependence of on the number of subtracted frequencies when we approach the noise level, which is represented by a dotted line. Thus these frequencies are not used in our analysis.

4.3.2. UBV data

On the 20th of July we observed PG 1618 in multifilter mode, i.e. with automatic filter changing between each measurement. The integration times of 9 s (U), 3 s (B) and 8 s (V) were chosen to have a similar S/N in the three bands. In this way we obtained three quasi-contemporary UBV light curves with an effective resolution time of 20 s in each band. The amplitude spectra of the UBV data are shown in Fig. 6. In order to obtain more precise amplitudes and phases, we applied a least-squares two-sinusoid fit to the data, using the frequencies derived from the no-filter observations (see previous section). The amplitudes have been then corrected taking into account the contribution of the F star; hence the values reported in Table 3 are relative to the flux of the sdB star only. The amplitude errors take into account both the fit errors and the flux indetermination due to the contamination of the F star. For completeness, Table 3 contains also the results of the V observation of July 19. One can note that the V amplitude of the secondary frequency in July 20 (2.6 mma) is much higher than that of July 19 (0.6 mma), whereas the amplitudes of the primary frequencies are the same. It is not clear weather this amplitude variation is real or due to the noise, which in the V band is almost at the same level of the signals. For this reason it might be more safe to scale the amplitude of the secondary frequency to that of the previous night and consider a value of 0.6 mma. The amplitude ratios and phase differences of PG 1618 can be a valuable contribution for the mode identification, as it has been demonstrated in the case of the  Cephei stars (see for example Cugier, Dziembowski & Pamyatnykh 1994; Heynderickx et al 1994; and ref. therein).

Fig. 6. UBV amplitude spectra of PG 1618, obtained from the PMT quasi-contemporary data of July 20, 1999. The vertical lines correspond to the main frequencies of the no-filter observations.

Table 3. UBV Pulsation Amplitudes and Phases¹.
Notes:
1) The normalized phases are referred to 0.0 UT of July 20, 1999.
2) Amplitudes and phases of July 19 (see the text)

As already mentioned in Sect. 4.2, PG 1618 was also observed in U, B and R bands with the CCD photometer in October 1999. The amplitude spectra are shown in Fig. 7. In the R spectrum, which is the most noisy due to cirrus, both signals do not exceed the noise level. In the U and B bands the spectra are different from those of July ³: the signal at 6.95 mHz, which was the strongest three months before, is close to the noise level, whereas the peak at 7.18 mHz has an amplitude increased by a factor of about 2. Hence the comparison between the results of July and October 1999 indicates that amplitude variations in time-scales of months could be present, in addition to the night to night changes observed in July.

Fig. 7. UBR amplitude spectra of PG 1618B, obtained from the CCD data of October 1999. The vertical lines correspond to the main frequencies of the no-filter observations.

© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000
helpdesk.link@springer.de