2 Observations and data reduction

2.1 The observations

The observations described in this paper result from multisite rapid photometry campaigns organized on three consecutive seasons in 1992, 1993 and 1994. The participating sites are listed in Table 1.

The data have been obtained with 2-channel or 3-channel photometers all equipped with blue sensitive photomultipliers (Hamamatsu R647-04 or similar) and used without a filter (white light). These instruments fulfill the specifications and requirements as prescribed by Kleinman et al. (1996). The sampling time was either 5 s or 10 s. In the former case, the data were coadded to 10 s afterwards. For 2-channel photometers, the observing procedure consists of simultaneously monitoring the target star in one channel and a comparison star in the second channel. The sky background is measured at random time intervals in both channels. For 3-channel photometers, the sky background is continuously monitored by the third channel, with the target and comparison stars placed in the other two channels.

2.2 Summary of the discovery data

After the announcement that RXJ 2117+3412 was a PG 1159 type star (Werner 1993; Motch et al. 1993), the star was immediately tested for photometric variability. It was found to be variable by Watson (1992) and Vauclair et al. (1993) independently. The data set obtained at the 2.5 m NOT is described in Vauclair et al. (1993). It was obtained with the Chevreton three-channel photometer - a short description is given in Vauclair et al. (1989). The data consist of 28 hr of time-series photometry accumulated during 4 consecutive nights, and allowed to extract 27 peaks in the power spectrum. The largest amplitude mode was found at 1217.8 $\mu$Hz (821 s period) with a 4.6 mma amplitude, after re-reduction of the data. The frequency resolution of these single-site discovery data was only 2.7 $\mu$Hz. Figure 1 shows the power spectrum of the light curve, re-reduced for the present paper.

Figure 1: Power spectrum of the discovery data re-reduced for the present paper. The corresponding window function is shown at the same frequency scale in the insert. Power is plotted in units of micro-modulation power ($\mu$mp) as a function of frequency (in $\mu$Hz) between 0 and 4000 $\mu$Hz.

Figure 2: Normalized light curve of RX J2117+3412 during the 1992 WET (XCOV8) campaign. The modulation intensity is plotted as a function of time (UT). Each panel corresponds to one day.

2.3 1992 WET campaign

A WET campaign had been planned for September 1992, shortly after the discovery of the variability of RXJ 2117+3412. The star was its third priority target. This campaign obtained 78 hr of non-redundant data. This WET campaign will be referred to as 1992 WET (or also XCOV8) in the following discussion. The observing sites involved are listed in Table 1. The total duration of the campaign was 10.7 days, with a corresponding frequency resolution in the Fourier transform of 1.1 $\mu$Hz. The coverage of the 1992 WET for RXJ 2117+3412 was 35%, a rather satisfactory coverage for a third priority target. The observation log is given in Table 2, and Fig. 2 shows the normalized light curve of the 1992 WET data.

2.4 1993 multisite campaign

A multisite campaign was organized, independently of the WET network, one year after the 1992 WET campaign. 105 hr of fast photometry were obtained during 9.1 days. The coverage was 48% and the frequency resolution achieved 1.3 $\mu$Hz. The sites involved are listed in Table 1 and the observation log is given in Table 3.

Surprisingly, the average amplitude of the pulsations observed during this campaign was much smaller than one year earlier. The normalized light curve of this campaign is shown in Fig. 3. Note that the vertical scale of Fig. 3 is the same as in Fig. 2.

Figure 3: Normalized light curve of RXJ 2117+3412 during the September 1993 campaign. The modulation intensity is plotted as a function of time (UT). Each panel corresponds to one day.

Figure 4: Normalized light curve of RXJ 2117+3412 during the 1994 WET (XCOV 11) campaign. The modulation intensity is plotted as a function of time (UT). Each panel corresponds to one day.

2.5 1994 WET campaign

RXJ 2117+3412 was the first priority target of the 1994 WET campaign. The observing sites involved are listed in Table 1 and the observation log is given in Table 4.

The campaign had a total duration of 15.0 days, of which only 13.8 days are used in the forthcoming reduction, implying a frequency resolution of 0.8 $\mu$Hz in the power spectrum. 175 hr of non-redundant data were obtained, leading to a coverage of 49%. The light curve, shown in Fig. 4, looks quite different from those of the two previous campaigns. Here, the largest amplitude mode is at a frequency of 958.5 $\mu$Hz (1043 s period). This campaign is referred to as 1994 WET (or also XCOV11) in the following text.

In addition to the data listed in Table 4, which were obtained with photomultiplier-based photometers, some CCD photometry data have been acquired at the Teide Observatory IAC 0.80 m telescope during part on the 1994 WET on three consecutive nights: 1994 August 9-11. Images of the RXJ 2117+3412 field were taken every 250 s, on average, with an exposure time of 150 s. Because of the different sampling time, the CCD data are reduced separately and are not included in the calculation of the power spectrum. They are useful for a comparison of the CCD photometry with photomultiplier photometry. Table 5 is the log of the CCD photometry observations.

 

Table 4: Journal of observations: 1994 WET (XCOV11).

Run Name	Telescope	Date	Start Time	Run Length
		(UT)	(UTC)	(s)
emcav-03	Maidanak 1 m	31 July 94	18:34:40	9750
emcav-04	Maidanak 1 m	1 August 94	16:56:40	10170
suh-0015	Suhora 60 cm	1 August 94	23:36:50	6010
gv-0414	TBL 2 m	2 August 94	00:54:00	8530
emcav-05	Maidanak 1 m	2 August 94	16:18:20	25010
suh-0016	Suhora 60 cm	2 August 94	22:20:30	12600
gv-0416	TBL 2 m	2 August 94	22:36:00	16300
sjk-0374	JKT 1 m	3 August 94	01:49:30	2990
sjk-0375	JKT 1 m	3 August 94	03:03:30	10310
emcav-06	Maidanak 1 m	3 August 94	16:14:00	24240
sjk-0376	JKT 1 m	3 August 94	21:11:30	22900
gv-0418	TBL 2 m	3 August 94	22:34:00	17340
sjk-0377	JKT 1 m	4 August 94	03:37:00	7640
pab-0179	Mauna Kea 24 $^{\prime\prime}$	4 August 94	09:29:10	19260
emcav-07	Maidanak 1 m	4 August 94	16:39:40	23820
suh-0017	Suhora 60 cm	4 August 94	20:16:30	18690
sjk-0378	JKT 1 m	4 August 94	21:33:00	17700
gv-0420	TBL 2 m	5 August 94	00:10:00	11570
sjk-0379	JKT 1 m	5 August 94	02:30:30	12290
pab-0182	Mauna Kea 24 $^{\prime\prime}$	5 August 94	07:12:00	27060
emcav-08	Maidanak 1 m	5 August 94	17:35:30	3530
emcav-10	Maidanak 1 m	5 August 94	18:38:30	5700
gv-0422	TBL 2 m	5 August 94	20:55:00	22930
suh-0018	Suhora 60 cm	5 August 94	21:07:00	16250
pab-0183	Mauna Kea 24 $^{\prime\prime}$	6 August 94	06:22:30	24330
pab-0184	Mauna Kea 24 $^{\prime\prime}$	6 August 94	13:15:30	5730
sjk-0380	JKT 1 m	6 August 94	21:07:30	6730
gv-0424	TBL 2 m	6 August 94	22:47:00	7400
sjk-0381	JKT 1 m	6 August 94	23:00:30	5060

 

Table 4: continued.

Run Name	Telescope	Date	Start Time	Run Length
		(UT)	(UTC)	(s)
pab-0185	Mauna Kea 24 $^{\prime\prime}$	7 August 94	06:15:00	30920
k44-0259	Kavalur 40 $^{\prime\prime}$	7 August 94	14:08:00	3220
k44-0260	Kavalur 40 $^{\prime\prime}$	7 August 94	15:17:40	23390
emcav-11	Maidanak 1 m	7 August 94	16:04:10	25870
sjk-0382	JKT 1 m	7 August 94	21:36:30	23050
gv-0445	TBL 2 m	7 August 94	22:40:00	16700
ra-340	McDonald 82 $^{\prime\prime}$	8 August 94	06:01:30	15200
pab-0186	Mauna Kea 24 $^{\prime\prime}$	8 August 94	06:30:10	23930
pab-0187	Mauna Kea 24 $^{\prime\prime}$	8 August 94	13:42:00	1770
emcav-12	Maidanak 1 m	8 August 94	16:01:40	26060
suh-0019	Suhora 60 cm	8 August 94	19:45:30	1940
sjk-0383	JKT 1 m	8 August 94	21:03:30	32000
gv-0426	TBL 2 m	8 August 94	22:07:00	18500
ra-341	McDonald 82 $^{\prime\prime}$	9 August 94	02:53:10	21410
pab-0188	Mauna Kea 24 $^{\prime\prime}$	9 August 94	06:38:10	29840
sh-0000	Wise 40 $^{\prime\prime}$	9 August 94	18:40:40	14690
suh-0020	Suhora 60 cm	9 August 94	23:26:00	9810
ra-342	McDonald 82 $^{\prime\prime}$	10 August 94	02:54:50	30450
pab-0189	Mauna Kea 24 $^{\prime\prime}$	10 August 94	06:16:30	31140
sh-0003	Wise 40 $^{\prime\prime}$	10 August 94	18:34:10	3650
sh-0004	Wise 40 $^{\prime\prime}$	10 August 94	20:02:00	2240
sh-0006	Wise 40 $^{\prime\prime}$	10 August 94	21:48:20	14860
ra-343	McDonald 82 $^{\prime\prime}$	11 August 94	05:30:20	21010
pab-0190	Mauna Kea 24 $^{\prime\prime}$	11 August 94	06:14:30	31300
sh-0007	Wise 40 $^{\prime\prime}$	11 August 94	18:13:30	24950
ra-344	McDonald 82 $^{\prime\prime}$	12 August 94	02:48:40	30740
ra-345	McDonald 107 $^{\prime\prime}$	13 August 94	05:05:50	6310
pab-0191	Mauna Kea 24 $^{\prime\prime}$	13 August 94	07:18:00	13490
ra-346	McDonald 107 $^{\prime\prime}$	13 August 94	09:00:50	8160
ra-347	McDonald 107 $^{\prime\prime}$	14 August 94	03:43:30	11760
ra-348	McDonald 107 $^{\prime\prime}$	14 August 94	07:04:10	2330
ra-349	McDonald 107 $^{\prime\prime}$	14 August 94	08:12:30	11620
gv-0472	Xinglong 2.16 m	14 August 94	12:31:00	25850
gv-0474	Xinglong 2.16 m	15 August 94	12:44:10	25890

2.6 Data reduction

The photomultiplier photometer data have been reduced in a now standard way (Nather et al. 1990; Kepler 1993). In both 2- and 3-channel photometers, the sky background is measured at the beginning and at the end of each run in all channels. This is used to determine the sensitivity ratios of the channels. In 3-channel photometric data, the sky background is monitored continuously in one channel, allowing for point by point subtraction of the sky background from the target and comparison star channels, after application of the proper sensitivity ratios. For 2-channel data, the sky background is normally measured at irregular intervals in both channels. The sky background is then constructed by polynomial interpolation. Each star channel is then corrected for extinction and normalized. When conditions show evidence for transparency variations, the normalized target star channel counts are divided by the smoothed comparison star channel counts. Subtracting unity from the resulting time series gives the time series on which the barycentric correction to the time base is applied.

Each of the observing campaigns has been reduced shortly after the observations. For the purpose of the present paper however, all the data have been re-reduced in an homogeneous way. A few runs have been rejected where the noise level was too high, which was usually due to clouds or instrumental problems. In case of overlapping data, we kept the best signal/noise ratio run in our analysis. The power spectrum of each time series is obtained by a Fourier Transform. A non-linear least-squares fitting routine (which fits the frequencies, amplitudes and phases of sine waves to the time series), followed by prewhitening, is used to extract the significant modes from the power spectra. The discovery data obtained in August 1992 at the NOT, were also re-reduced for comparison with the original reduction, although these data were not used in the present paper because they are single site data with too poor a frequency resolution. The power spectrum of these data is shown in Fig. 1. The power spectra of the time series obtained during the 1992 WET, the 1993 multisite campaign and the 1994 WET runs are shown in Figs. 5-7 respectively. Figure 8 illustrates the prewhitening sequence on a portion of the 1994 WET power spectrum.

 

Table 5: Journal of the CCD photometry obtained at the IAC 80 cm telescope.

Date	Start time	Run length*
(UT)	(UTC)	(s)
August 9, 1994	22:33:42	22250
August 10, 1994	22:57:12	24500
August 11, 1994	23:09:39	24750

Note. ^* The run lengths are the total lengths of the runs which consist in series of 150 s exposure time on RXJ 2117+3412 field taken every 250 s in average.

Power is seen without ambiguity in the range 650 $\mu$Hz-4340 $\mu$Hz. Most of the peaks with significant power are found in the restricted range 650 $\mu$Hz-1600 $\mu$Hz. For each observing season, Table 6 lists the frequencies f, with their uncertainties $\delta$f (in $\mu$Hz) and the amplitudes A (in mma) of the peaks considered significant in the power spectra. These values are derived by the non-linear least squares fit. To decide whether a peak in a power spectrum is significant on an objective basis, the following rules were applied: a False Alarm Probability (FAP) (Kepler 1993) was estimated on the 1000 $\mu$Hz frequency range embedding most of the significant power. All peaks with a $FAP \leq$ 10^-3 were considered as significant. Several peaks with FAP >10^-3were also included in the list (marked with colons in Table 6), but only if: i) they fit the pattern of rotationally split multiplets, or ii) they fit the period spacing ($\Delta P$) distribution, or iii) they have frequency equal to, or close enough to, the frequency of a significant peak observed in other seasons.

CCD photometry obtained at the IAC 0.80 m telescope has been reduced independently. The images were taken without a filter. The basic reductions (bias subtraction and flatfield corrections) were made by use of the IRAF package. The photometric reductions were done using the MOMF package (Kjeldsen & Frandsen 1992). The resulting time series was analyzed by a non-linear least-squares fit. Frequencies extracted from this data set are listed in Table 7.

Figure 5: Power spectrum of the 1992 WET (XCOV 8) light curve. The units are the same as in Fig. 1. Note the different vertical scale on each panel. The window function is shown at the same frequency scale in the insert. The prominent sidelobes in the window function correspond to the 1 and 2 day aliases.

Figure 6: Power spectrum of the 1993 light curve. The units are the same as in Fig. 1. Note the different vertical scale on each panel. The window function is shown at the same frequency scale in the insert. The prominent sidelobes in the window function correspond to the 1 day alias.

Figure 7: Power spectrum of the 1994 WET (XCOV 11) light curve. The units are the same as in Fig. 1. Note the different vertical scale on each panel. The window function is shown at the same frequency scale in the insert. Note the small amplitude of the 1 day alias sidelobes.

Figure 8: Illustration of the prewhitening sequence. This figure is an enlarged part of the power spectrum of the 1994 WET shown in Fig. 7, restricted to the frequency range 750-1250 $\mu$Hz, where most of the weak peaks appear. The five panels illustrate (from top to bottom) the successive steps by which the largest amplitude peaks are removed from the data. Those frequencies removed at each step are marked with thick arrows. Note in panel 3 the peaks at 1023.684 $\mu$Hz and at 1045.944 $\mu$Hz that are not significant in this run taken alone, according to our False Alarm Probability (FAP) criterion. However, since these two peaks are unambiguously present in the 1992 data, they are considered as real peaks and kept in the prewhitening procedure. Panel 5 shows what is left after removing of all the significant power. Three peaks are marked with arrows: 840.367 $\mu$Hz, 988.726 $\mu$Hz and 1123.747 $\mu$Hz. These peaks are not significant on their own, according to our adopted FAP criterion. However, they fit the known rotational frequency splitting or period spacing (1123.747 $\mu$Hz) pattern. We include them in Table 6, but denote them with a colon to indicate their lesser certainty.

 

Table 6: Combined list of the frequencies identified in RXJ2117+3412.

	1994			1993			1992
	WET						WET
f	$\delta f$	A	f	$\delta f$	A	f	$\delta f$	A
653.987	0.018	0.90				653.811	0.029	1.46
						655.556	0.031	1.33
666.938	0.028	0.57:
						706.260	0.039	0.98:
717.714	0.008	1.96
789.042	0.022	0.71
793.783	0.019	0.84
830.708	0.006	2.68				831.412	0.022	1.78
836.067	0.022	0.74	835.000	0.040	0.66
840.367	0.040	0.43:
			851.483	0.041	0.64
872.337	0.029	0.55
						889.587	0.033	1.23
						894.800	0.019	2.16
906.378	0.016	1.03
921.721	0.031	0.53
940.563	0.020	0.82	939.838	0.063	0.43:	939.948	0.051	0.89
						945.156	0.040	1.05
949.909	0.022	0.83				950.445	0.022	2.07
958.533	0.005	3.64	957.959	0.042	0.65
963.282	0.025	0.67	963.416	0.031	0.86
978.874	0.032	0.52
988.726	0.038	0.44:
1005.645	0.033	0.49
1010.541	0.032	0.52
1023.684	0.037	0.45	1023.292	0.029	0.90	1023.594	0.020	2.03
1045.944	0.050	0.35:	1044.904	0.072	0.36:	1045.690	0.045	0.90
1055.703	0.042	0.41
1096.712	0.016	1.05	1096.060	0.055	0.52
1101.942	0.039	0.41				1101.203	0.065	0.67:
			1107.300	0.063	0.46	1107.224	0.027	1.61
1123.747	0.049	0.32:
1179.955	0.007	2.16	1179.761	0.061	0.43	1179.893	0.029	1.43
						1190.578	0.054	0.79:

 

Table 6: continued.

	1994			1993			1992
	WET						WET
f	$\delta f$	A	f	$\delta f$	A	f	$\delta f$	A
1212.490	0.016	0.95	1212.419	0.047	0.58
1217.812	0.012	1.38	1217.886	0.022	1.21	1217.865	0.010	4.07
			1245.457	0.059	0.46
1289.129	0.035	0.45	1289.136	0.060	0.45	1289.160	0.015	2.63
1315.055	0.012	1.24	1315.032	0.021	1.26	1315.181	0.026	1.55
1362.734	0.056	0.29:	1362.495	0.074	0.36
1397.385	0.057	0.28:	1397.242	0.061	0.45
1439.198	0.025	0.62
1539.991	0.055	0.29:
1548.653	0.043	0.37
						1549.959	0.050	0.75
			1572.012	0.094	0.27
1947.334	0.068	0.26:
1956.008	0.027	0.58	1956.785	0.103	0.29
1968.952	0.023	0.67	1968.222	0.085	0.35	1968.915	0.047	0.84
						2109.129	0.049	0.76
2133.259	0.064	0.25:	2133.122	0.055	0.47
			2143.374	0.124	0.21:
			2153.980	0.079	0.33
			2164.116	0.122	0.21:
			2174.884	0.076	0.35
			2184.777	0.110	0.23:
			2402.113	0.098	0.26
3408.257	0.046	0.35
3517.490	0.049	0.30
3924.971	0.062	0.27
						4077.942	0.100	0.41
			4308.046	0.074	0.35
			4339.147	0.132	0.20: