In previous analyses of 57 Tau (e.g., Fu Jian-ning et al. [1996]), differences in the nightly mean magnitude of 57 Tau, relative to the comparison star, have been mentioned, but not discussed in depth. After applying the nightly determined extinction coefficient, a nightly zero-point adjustment was made, which was thought to be caused by unknown observational problems. In our analysis we were interested in the thorough study of the low frequency domain of the spectrum, since all the available data sets displayed regular features in this range (Paparó et al. [1999]).

Since the variability of the comparison star and the incorrect transformation of the instrumental systems may effect our conclusions for the mean light level of 57 Tau, both the constancy of the comparison stars, and the effect of data's homogenizations were carefully investigated.

3.1 Comparison stars

The constancy check of the comparison star, HR 1358, is based on the simultaneous observation of HR 1358 and HR 1430 in the course of the multi-site campaign on 57 Tau in 1995 in Spain and Mexico. Over 14 nights, 54.35 hours, 543 Strömgren uvby measurements were collected. The nightly average values versus the mean time of the given observing run are shown in Fig. 1. The Spanish data are marked by filled squares and the Mexican ones by crosses.

The average Strömgren values of the differential magnitudes for $\rm HR~1430-HR~1358$ for all data, from the Spanish and Mexican data sets, are listed in Table 2. The ubvy values taken from Mermilliod et al. ([1997]) are given at the bottom of the table.

**Table 2:** Mean values of $\rm HR~1430-HR~1358$
Data	N	u	v	b	y
All	543	$-0.7726 \pm .0002$	$-1.0153 \pm .0001$	$-0.8948 \pm .0001$	$-0.7496 \pm .0001$
Spanish	473	$-0.7725 \pm .0002$	$-1.0154 \pm .0001$	$-0.8948 \pm .0001$	$-0.7496 \pm .0001$
Mexican	70	$-0.7733 \pm .0008$	$-1.0151 \pm .0004$	$0.8950 \pm .0003$	$-0.7492 \pm .0004$
Catalogue		-.764	-1.025	-0.908	-0.768

The mean values are given with high accuracy. The standard deviation of the measurements around the mean, $\approx~0\hbox{$.\!\!^{\rm m}$ }003$ in vby colours and $\approx~0\hbox{$.\!\!^{\rm m}$ }005$ in u colour, could be regarded as the error of observations in 1995. The Spanish and Mexican mean values do not greatly differ which means that the two instrumental photometric systems are very close to each other. This is not surprising since the detector attached to both telescopes is the Danish photometer. The difference, concerning the catalogue values, is probably due to the difference of the instrumental and standard Strömgren systems.

While the low values of errors for the comparison stars suggest constancy of both comparison stars, a frequency analysis of $\rm HR~1430-HR~1358$ differences was carried out in a range of 0 - 50 cycles per day. The amplitude spectrum in y colour is given in Fig. 2. The amplitude spectra (A(f)) are characterized by its mean values < A(f) > i.e. 0.408 $\pm$ 0.213, 0.243 $\pm$ 0.135, 0.216 $\pm$ 0.119 and 0.255 $\pm$ 0.137 mmag in the uvby colours, respectively. Although for the most part, the amplitude spectrum does not show regular structure, a peak might be present in vby at 3.028, 3.025 and 3.022 c/d frequency with an amplitude of 0.90, 0.72 and 0.98 mmag, respectively.

The spectral window pattern, due to the multi-site observation, is not seen around this peak. The significance limit, 4 times the mean value of the residual spectrum (Breger et al. [1993]), has been accepted, and is 0.94, 0.83 and 0.96 mmag in vby, respectively. The distinct peak is only above the significance limit for the y colour.

Could this periodicity be caused by a difference in the mean light level between the two sites separated by 8 hours in longitude? As Table 2 and Fig. 1 show, the mean values of $\rm HR~1430-HR~1358$ are the same for both observatories with slightly larger scatter for the Mexican observations caused by the shortness of the data set. If the periodicity at 3.02 c/d is caused by some special instrumental circumstances at the different sites, the separate data would not show the periodicity. A periodicity at 3.026 c/d (with an amplitude of 0.96 mmag) with a spectral window pattern around it, has been found for the Spanish data. According to the significance test, the amplitude of the period is below the significance level (1.04 mmag). The Mexican data are too short for separately checking the period.

Instrumental magnitudes are often contaminated by small nightly trends, e.g., due to the errors in the extinction coefficients. To estimate the possible spectral distribution of this noise, trend-spectra were introduced by Kolláth & Paparó ([1999]). These spectra are given for two extreme cases: for uncorrelated trends and for systematic trends. In the first case the mean spectrum behaves like a coloured noise (continuous spectrum), while for systematic errors the peaks from the spectral window appear also in the trend spectrum. In general the spectral noise generated by the trends are between these two specific cases. We have to note that the trend spectra give no information on the amplitude of the noise due to the trends. Like the spectral window it gives the normalized spectral distribution only.

In Fig. 3. both the uncorrelated trend-spectra (UTS, thick curve) and the systematic trend-spectra (STS, thin curve) are displayed for the whole data set and also for the 1995 data. Both panels show that the effect of errors in the extinction coefficients is most pronounced around 3 c/d frequency values. A similar conclusion has been obtained by Poretti & Zerbi ([1993]) and Breger & Beichbuchner ([1996]) The 3.02 c/d frequency in the comparison light-curve is therefore probably related to errors in extinction correction.

We conclude that the differential light curve of the two comparison stars, $\rm HR~1430-HR~1358$ , does not show any evidence for variability, although it is slightly effected by extremely small errors in the atmospheric extinction coefficient. Any periodicity in the differential light curve of 57 Tau and HR 1358 should be attributed to 57 Tau as intrinsic variability.

3.2 Homogenization of data

Combining all of the 57 Tau data is not a trivial task. We have the advantage of similar spectral type comparison stars, so the colour dependence of instrumental systems can be neglected. In the milli-magnitude range, however, different photometer/filter combinations lead to different zero-points, even if the same comparison stars are used. This fact needs to be considered when different data sets from different locations are combined. A complicating factor is that, not only are Johnson V & Strömgren y data involved in our analyses, but Strömgren b colour data were also included.

In order to combine the data from the different sites adjustments were made. For each observatory the photometric zero-point of 57 Tau relative to HR 1358 was determined by averaging all the the data from each observatory. The mean values obtained are listed in Table 3.

**Table 3:** Mean values of 57 Tau - HR 1358 for different sites
Sites	N	mean values
Hungarian Johnson V	1039	-0.6081
Chinese Johnson V	322	-0.57106
Spanish + Mexican Strömgren y	948	-0.57460
Spanish + Mexican Strömgren b	948	-0.70195
McNamara Strömgren b	934	-0.79442

In order to get the highest possible frequency resolution, we treated all the observational data together, regardless of the filters used for the measurements. All the available data (even B.J. McNamara's Strömgren b colour data) are shifted to the mean value of the Spanish + Mexican Strömgren y colour. Shifts of $+0\hbox{$.\!\!^{\rm m}$ }0335$ , $-0\hbox{$.\!\!^{\rm m}$ }00354$ and $+0\hbox{$.\!\!^{\rm m}$ }21982$ were applied for the Hungarian & Chinese Johnson V, and B.J. McNamara's Strömgren b data. Johnson V & Strömgren y and b measurements were regarded to be identical except for the different zero-points.

The largest error introduced in our Fourier spectra is due to the mixing of the early b data with the later y or V observations. We have estimated this spectral noise by the following experiment: We made a synthetic signal with a single frequency with the highest amplitude (2 mmag) from the real data, but we increased the amplitude of the signal by 40 percent and shifted the phase by $10^\circ$ for the times of b observations (overestimated the generally obtained amplitude ratio and phase differences between the y and b colours). Then we treated these data like the real observations: we prewhitened the synthetic light-curve with the average amplitude (obtained by least-square fitting). The spectra of the test signal and the prewhitened data are displayed in Fig. 4. From this test it can be concluded that even with a 40 percent difference in the amplitudes and $10^\circ$ difference in phases the spectral residual is no more than 0.3 mmag for the highest amplitude component. More complicated cases (more frequencies, even not all excited simultaneously) are going to be discussed by Kolláth & Paparó ([1999]).

Our test, in this ideal case, proved that we can extend the time-base of the analysis for the B.J. McNamara's observations obtained in the early eighties for the Strömgren b colour for finding the periodicities in the star.

In the final step, B.J. McNamara's Strömgren b observations were shifted to the Spanish & Mexican mean value of Strömgren b colour for determining the amplitude of the pulsation frequencies in b colour. The shift ( $0\hbox{$.\!\!^{\rm m}$ }09247$ ) between the two Strömgren systems is much larger than expected for well-defined Strömgren systems. No trivial explanation exists but different photomultiplier tubes were employed at these sites and much of the difference is thought to arise from this fact.

As a result of this process, the low-frequency part of the amplitude spectrum is cleaned and any dominant periodicity in this range is unlikely to be caused by the inhomogeneity of different data sets.

**Table 4:** Frequency solutions for the subsets of data
		Frequency in c/d, Amplitude in mmag
Subset	Nights	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂
	N	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀	A₁₁	A₁₂
81/82	14	0.654^*	0.804^*	1.021	7.232^*	14.762	16.594	19.048	18.260^*	-	20.406^*	25.556	29.837^*
	762	2.13	2.80	1.14	1.90	2.07	1.60	2.18	1.06	-	2.40	1.68	1.88
86/87	9	0.659^*	0.845^*	-	6.262	-	16.626	18.202^*	-	-	20.411	25.843^*	-
	648	0.96	1.12	-	1.40	-	1.78	3.40	-	-	1.23	1.77	-
89	14	0.626^*	0.802^*	1.119	8.002	-	16.493	-	18.247^*	-	21.434^*	-	29.527
	627	1.25	1.89	1.93	1.26	-	1.58	-	3.76	-	2.21	-	1.24
95	14	0.665^*	0.813^*	-	7.237	14.173	16.214	-	18.230^*	-	20.446^*	-	29.843^*
	948	0.89	2.51	-	0.94	0.68	2.50	-	2.73	-	0.96	-	1.35
Hung.	16	0.657^*	0.831^*	-	7.094	14.597	16.232	18.201^*	-	-	20.429	24.800	29.866
	1039	1.20	2.00	-	1.41	1.25	1.66	2.61	-	-	1.53	1.75	1.19
Chin.	9	1.628	0.785	1.131^*	6.596	-	16.489	-	18.235^*	-	20.438^*	25.758	-
	322	0.97	1.57	2.35	0.96	-	1.44	-	3.87	-	2.94	1.10	-
81-87	26	0.657^*	0.803^*	1.162	7.093	-	-	18.011^*	18.258^*	18.403^*	20.416^*	25.841	29.836
	1668	1.90	1.79	1.38	1.21	-	-	2.11	1.32	1.36	1.37	1.36	1.23
86-89	23	-	0.803^*	1.118	-	-	16.232	18.201^*	-	-	20.413	26.673	-
	1275	-	2.04	1.64	-	-	1.55	2.60	-	-	1.84	1.26	-
81-89	40	0.660^*	0.793^*	1.122	7.019^*	-	17.615	18.216^*	18.260^*	-	20.441^*	25.553^*	29.836^*
	2295	1.89	1.40	1.61	1.00	-	1.49	1.60	1.57	-	1.62	1.31	1.31
81-95	54	0.657^*	0.803^*	1.119^*	7.223^*	14.161	16.738	18.220^*	17.257^*	20.218	20.441^*	24.555^*	29.839^*
	3243	1.26	1.80	1.07	1.00	0.95	1.06	1.41	2.07	1.35	1.24	1.13	1.29
81&95 b	30	0.657^*	0.805^*	-	7.233^*	15.189	16.739	-	17.248^*	18.472	20.406^*	24.555^*	29.838^*
	1882	1.21	3.01	-	1.38	1.60	0.93	-	2.11	1.27	1.68	1.56	1.51
^* The frequency can be localized in the original spectrum of the subset.

3.3 Mean light level of 57 Tau

The nightly mean photometric value (in a given filter) of 57 Tau, relative to the comparison star, HR 1358, versus the mean time of an observing run for each site was checked for periodicity. The method of averaging is useful if the periodicity is larger than an observing run, and seems to be stable if the pulsational periods are remarkably shorter, many cycles are averaged in a run.

A simple view of the mean light level does not show a cyclic pattern. After homogenization, the Strömgren y & b mean values of 57 $\rm Tau-HR~1358$ are $-0.5744 \pm 0.0019$ and $-0.7020 \pm 0.0027$ , respectively. The low value of the scatter for the mean light level suggests that if there is any variability, it has a low amplitude or periodicity near to 1 c/d.

A frequency analysis of the mean light values was carried out in a range of 0-4 cycles/day. A peak of highest amplitude at 0.80866 $(0\hbox{$.\!\!^{\rm m}$ }00163)$ and 0.80231 $(0\hbox{$.\!\!^{\rm m}$ }00318)$ cycles/day was found in y & b, respectively. According to a significance test, the periodicity is significant.

Although the amplitude of mean light level variation seems to be extremely low, it is comparable to the amplitude of the pulsation modes of 57 Tau, as shown in Fig. 5.

$\begin{figure} \resizebox{\hsize}{!}{\rotatebox{0}{\includegraphics{ds8700f5.ep... ...resizebox{\hsize}{!}{\rotatebox{0}{\includegraphics{ds8700f6.eps}}} \end{figure}$

Figure 5: The spectral window, the unprewhitened and residual amplitude spectrum of 57 Tau for the whole data set (1981-95). The amplitudes in the low frequency part are comparable to the amplitude of pulsation modes in the p-mode region. The low frequency part of the residual spectrum seems to be completely clean. The residual spectrum has a significant peak at 29.8386 c/d with large amplitude fluctuations

The final frequencies connected to the mean light level variation of 57 Tau were obtained as part of the final frequency solution given in the next paragraph.