8 Conclusions

We have demonstrated that the simultaneous photometry provides us with a very firm foundation: we have used the frequency solution found from photometry to limit the number of free parameters and thus we have obtained very accurate oscillation amplitudes in $\Lambda ^{{\rm H}\alpha }$ . This allows us to directly compare with the photometric amplitudes and to establish reliable amplitude ratios, that reflect the geometry of the mode and hence enable us to characterize the modes.

BN Cnc is the first case of a rapidly rotating $\delta$ Scuti star where we have been able to identify with some certainty the nature of the modes. Two modes have low values of the $R_{\alpha}$ ratio and are candidates for radial modes. They turn out to have the right frequency ratio for the mass and distance derived earlier by Hernandez et al. (1998). Three modes pose as low order non-radial modes, probably $\ell =1$ , because there are only two radial modes in the frequency range and $\ell = 2$ or higher degrees normally come out with low photometric amplitudes. Finally, the last mode is of higher degree, probably $\ell = 2$ as it is detected photometrically with an amplitude 3-4 times lower than the other modes we see. The suggested identifications need verification by other methods as in the case of FG Vir, where the two methods applied agree in 7 out of 8 cases.

We find indications of undetected modes, both in photometry and spectroscopy. These may well be high order modes, since their signatures are slightly more visible at the higher noise levels of the spectroscopy.

The constraints on the duty cycle proved to be severe for sites with smaller telescopes or low instrument efficiency which caused a degradation of S/N. For the planning of future campaigns it is very important to consider this in great detail to ascertain that the time allocated is used in the most efficient way.

Acknowledgements

Nordic Optical Telescope is operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
The data presented here have been taken using ALFOSC, which is owned by the Instituto de Astrofisica de Andalucia (IAA) and operated at the Nordic Optical Telescope under agreement between IAA and the NBIfAFG of the Astronomical Observatory of Copenhagen
THD acknowledges support from the Danish Space Board under the Danish Ministery of Research, J.nr. 456-9601878.
GH's observations were partially supported by the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung under grant S7304.

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