7 What's new?

The result of our analysis is an unambiguous determination of a small set of frequencies in BN and BV Cnc, and a low upper limit on the amplitudes of possible additional modes. We now comment in detail the frequency spectra of both stars and compare them with previous studies.

7.1 BN Cnc

For this star we detect six modes. Five of them were known before and only one additional mode (F6) is new in comparison to earlier measurements (Belmonte et al. 1994; Arentoft et al. 1998). With the new dataset any alias problems have disappeared. Even though the sidelobes are still there, the S/N (see Table 2) is so good that there is no room for ambiguity. The frequency resolution is so high that it is improbable that any unresolved modes will be found.

 

 

Table 2: Modes detected in BN Cnc. The frequencies, phases, and S/Nvalues refer to the combined 1997 and 1998 data. The 1992 amplitudes come from the Arentoft's et al. (1998) reanalysis of the STEPHI 1992 observations (Belmonte et al. 1994). The frequencies labeled as $\nu$(97) and former ID were taken from Table 4 of Arentoft et al. (1998). Errors are given in parentheses for the last digits.

Our	Former	Frequency		Amplitudes [mmag]				Phase		$\nu$(97)
ID	ID	[d-1]	[$\mu$Hz]	1992	1997	1998	1997+1998	[rad]	S/N	[$\mu$Hz]
F1	A4	25.76114(04)	298.1614(05)	2.0	2.00(27)	3.01(8)	2.92(7)	4.87(03)	26	298.01
F2	A2	23.02981(05)	266.5487(05)	2.1	2.08(26)	2.52(8)	2.48(7)	1.70(03)	20	266.42
F3	A8	28.27039(05)	327.2036(05)	2.7	1.99(23)	2.42(8)	2.38(7)	3.08(03)	23	327.16
F4	A1	22.78352(05)	263.6981(06)	1.2	1.80(27)	2.32(8)	2.29(7)	5.08(03)	17	263.69
F5	A5	25.93964(05)	300.2273(06)	0.9	2.33(25)	2.13(8)	2.13(7)	3.87(03)	24	300.24
F6	-	25.43666(17)	294.4057(19)	--	0.92(24)	0.63(8)	0.67(7)	1.88(11)	6	--

Table 2 lists the modes we have detected with references to the analysis of Arentoft et al. (1998) indicated. Within the uncertainities, the amplitudes of the five dominant modes (except maybe F1) seem to be constant from 1997 to 1998. Two modes (F4 and F5) were weaker during the STEPHI campaign in 1992 and have increased amplitudes by roughly a factor of two. STEPHI had one more significant mode (A3) which, however, is different from the F6 mode. Two additional frequencies (A6 and A7) are listed by Arentoft et al. (1998), both with S/N < 3.0 in 1997 data, and none of them was recovered in the present larger dataset.

The noise level we obtained is around 0.12 mmag on the short side of the oscillation frequencies in the interval 8-15 d^-1 and decreases to a white noise level of 0.07 mmag around 45 d^-1. Modes with amplitudes above 0.5 mmag should be therefore detectable. For the rereduction of the STEPHI data, the corresponding noise levels were 0.17 mmag and 0.11 mmag (Arentoft et al. 1998). After removal of six modes, the residuals show only a small excess just below 30 d^-1, indicating either some non-detected modes or perhaps inadequate removal of the signal. If there were indeed more modes with amplitudes just below the detection limit, including these modes into the solution would probably change the results for the largest-amplitude modes in an unsignificant way.

By varying weights and by adding a few more modes, we have found rough estimates of the systematic errors on the detected modes. From Table 4 it follows, using the relation $\sigma_{\rm amp} = \sqrt{\pi\sigma_{\rm rms}^2/N}$, that not counting points with low weights and taking N = 6000 and $\sigma_{\rm rms}$ = 0.003 mmag, we get a noise in the amplitude spectrum of $\sigma_{\rm amp}\sim$ 0.07 mmag. With the typical amplitude of the modes in BN Cnc of 2.5 mmag, we expect a $S/N \sim 35$ or an error in the amplitudes of 3%. The S/N in Table 2 are derived from an averaged noise in the residual amplitude spectrum. The values in Table 2 are lower than 35, because of the excess power in the range of the pulsation modes compared to the high frequency part of the spectrum.

Montgomery and O'Donoghue (1999) have derived analytical error formulas for least squares fits. With the same parameters as above and T = 10 months we find using their Eqs. (4), (10) and (11): $\sigma(a) = 0.055$ mmag, $\sigma(f) = 0.0005$ $\mu$Hz and $\sigma(\phi) = 0.022$ rad. The errors of the amplitude, frequency and phase given in Table 2 are only slightly higher than those obtained from the analytical predictions.

7.2 BV Cnc

This star was shown to be a multimode $\delta$ Scuti star by Arentoft et al. (1998), where four modes are listed. We have reanalyzed the 1997 data and found somewhat lower amplitudes (see Table 3). One night was rejected and the remaining nights were detrended to remove obvious drift problems. New weights were calculated and bad points rejected. Arentoft et al. (1998) also cleaned the data before deriving their amplitudes.

In 1998 data we find three frequencies (Fig. 8). Owing to the low amplitudes and the shape of our spectral window, an 1 d^-1ambiguity in the derived frequencies remains. The frequencies F1 to F3 reported in Table 3 were derived from the combined 1997 and 1998 dataset and then refined by the non-linear least-squares. At the residual periodograms of 1998 data (bottom ones in Fig. 8), F4 can be barely visible. It is, however, obvious that this frequency was present in 1997 data, which can be judged from the bottom panel of Fig. 9 showing the periodogram for 1997 data after removing the first three frequencies. Therefore, we included F4 = 20.246 d^-1, which is an 1 d^-1alias of A3 derived by Arentoft et al. (1998), as the fourth frequency for BV Cnc.

At the same time, we can clearly see (Fig. 9, Table 3) that not only F4, but amplitudes of all four modes have decreased between 1997 and 1998. In addition, more low-amplitude ($A \le$ 0.5 mmag) modes can be present in the 1998 data because of the excess of power at the residual periodograms (Fig. 8) in the range between 15 and 28 d^-1. Their amplitudes are close to the detection limit, so we can only indicate the most promising candidate. This is the peak at frequency of 17.77 d^-1.

 

 

Table 3: Modes detected in BV Cnc. The F4 frequency was derived from the 1997 data only, while frequencies F1 to F3 from the combined 1997 and 1998 data after prewhitening them with F4. Phases and S/N values were derived from the fit to the 1998 data only. The frequencies labeled as $\nu$(97) were taken from Table 5 of Arentoft et al. (1998). Former ID come also from that paper. Errors are given in parentheses for the last digits.

Our	Former	Frequency		Amplitudes [mmag]		Phase		$\nu$(97)
ID	ID	[d-1]	[$\mu$Hz]	1997	1998	[rad]	S/N	[$\mu$Hz]
F1	A1	16.45039(06)	190.3980(07)	2.21(26)	1.45(9)	0.33(06)	7.1	190.47
F2	A2 alias	16.73053(08)	193.6404(09)	1.47(25)	1.08(9)	2.60(08)	5.3	204.83
F3	A4 alias	32.90896(10)	380.8907(12)	1.15(23)	0.79(8)	5.30(11)	4.9	369.10
F4	A3 alias	20.246(4)	234.33(5)	2.18(23)	0.52(8)	4.77(16)	3.7	222.65

Figure 9: The evidence for the amplitude change in BV Cnc. Top: LS amplitude spectrum for 1998 data from analysis 2. Middle: the same for 1997 data. Bottom: LS amplitude periodogram of the 1997 data after removing the F1 to F3 frequencies. Note that F4 = 20.246 d-1 clearly stands above the noise level.