8 Discussion

The results fall in two categories: the technical or observational aspects and the scientific progress made in this project.

8.1 On the differential CCD photometry

Table 4 presents two values for the rms deviation of each datapoint from the final solution for the lightcurve of BN Cnc for each site, as well as the total weight of the dataset as applied in the analysis of the combined time series. The first rms entry is calculated giving equal weight to each point, whereas the second applies the weight used for analysing the lightcurve. Poor measurements enter fully into the first, but are eliminated in the second value. The difference reflects the extent to which the data has been cleaned and weighted.

 

 

Table 4: Postfit mean residual standard deviation calculated for all observations from a given site without (RSD₁) and with (RSD₂) weights applied. The last column is the sum of all weights for observations made at a given site presented as a percentage of the summed weights for all observations. The numbers were calculated for the combined 1997 and 1998 dataset for BN Cnc and analysis 1.

Observatory	RSD1	RSD2	Contr.
	[mmag]	[mmag]	%
Tenerife	2.91	2.13	32.0%
Arizona APT	5.61	3.35	17.5%
Konkoly (60 cm)	2.89	2.42	12.3%
Konkoly (100 cm)	4.95	3.49	8.5%
Bia ków	3.85	3.44	8.2%
Sutherland	5.44	3.03	5.5%
ESO	4.87	3.97	4.0%
La Palma	4.95	3.45	1.5%
UPSO	8.79	--	0.4%
Odessa	12.08	--	0.2%
OHP	--	--	0.0%
1998 data	4.55	2.88	90.1%
1997 data	3.94	3.11	9.9%

Looking at Table 4 it is evident that a few sites dominate, partly because of the number of contributed nights, but also due to a higher accuracy for each datapoint.

A few participating sites did not reach the expected accuracy. The distributed observational guidelines obviously were not well enough prepared, that all sites understood the procedures that need to be followed in order to get high quality data. In some cases the instrumentation was not adequate (no autoguider, no overscan of the CCD etc.).

It is also evident that the best CCD photometry outperforms the APT with a photoelectric photometer, which is how it ought to be given that the quantum efficiency of CCDs are higher than for photomultipliers. The factor is, however, small enough that the Arizona site at a different longitude than the CCD sites is very important, not to mention its ease of use. It must be also kept in mind that weather conditions in Arizona were below normal. The value from the third column of Table 4 corresponds well with the values quoted in Sect. 3 obtained for other $\delta$ Scuti stars observed with the APT in Arizona.

The sites providing multicolour data show a better S/N in the blue bands. It seems to be an advantage to observe in the B (or b) band instead of the V (or y) band. The increase in oscillation amplitude going from V to B makes up for the loss of the number of photons.

The window function we obtained (Fig. 7) does not really look like a multisite window function. The alias problem is anyway solved for BN Cnc star due to the presence of data distributed over several months and the low noise level achieved. The high frequency resolution obtained almost guarantees that all detected modes are single.

8.2 Results for the two stars

The noise level in the resulting spectra has been lowered in comparison with earlier observations. It is comparable to the best measurements of other $\delta$ Scuti stars. The mode content of the two stars is consequently better defined than before. The presence of some of the modes seen by Arentoft et al. (1998) in the BN Cnc data has not been confirmed. This is important because the parameters derived for BN Cnc depended on these presently undetected modes. This is described in more detail in Paper II.

The amplitudes, frequencies and phases of the six BN Cnc modes are very well determined and provide an excellent baseline for the subsequent analysis of the spectroscopic timeseries presented in Paper II. There is a small bump in the residual noise spectrum in the range 26-30 d^-1 for this star, but it is difficult to detect any unambiguous modes explaining the presence of this bump.

Evidently the amplitudes of BV Cnc modes have decreased from 1997 to 1998 which is probably best documented by Fig. 9. The difference diminished slightly when a reanalysis was done of the original 1997 data, but the change still remains at a non-ambiguous level. In BV Cnc the presence of several modes close to the detection limit is indicated by a very non-flat residual noise spectrum (see Fig. 8). Opposite to the case of BN Cnc, and due to the low amplitudes we measure, alias problems are quite severe.

It is interesting to note that for BV Cnc the difference between F3 and doubled F1 frequency is very small and amounts to 0.00822 $\pm$.00016 d^-1. This is almost exactly equal to 3 yr^-1 = 0.00821 d^-1. Since it could happen that both F1 and F3 are in error by 1 or 2 yr^-1, the possibility that F3 is a harmonic of F1 cannot be rejected. In that case the star would be quite unusual because harmonics are rarely observed for such low-amplitude pulsations. In case it is a pure coincidence, the two modes are very close to the 2:1 resonance which may play an important role in their behaviour.

It should be also pointed out that the two faintest $\delta$ Scuti stars in Praesepe, BS Cnc observed by STEPHI (Hernández et al. 1998a) and BV Cnc, display a very similar pattern of excited modes. Both have two or three modes in the range between 15 and 20 d^-1 and a single mode with frequency over 30 d^-1. In other words, BV Cnc matches the pattern of the luminosity dependence of the frequencies excited in Praesepe $\delta$ Scuti stars, shown by Belmonte et al. (1997). This means that studying $\delta$ Scuti stars in open clusters, especially in Praesepe, could indeed help us to understand the nature of mode selection, constrain cluster parameters and support the mode identification. For this purpose, the work on the other, less extensively observed $\delta$ Scuti stars in Praesepe, need to be continued.