N ov 1 99 7 The frequency content of Double – Mode Cepheids light curves and the importance of the cross – coupling terms

The recent results obtained on the frequency content of Double–Mode Cepheids light curves and the properties of their Fourier parameters are reviewed. Some points briefly discussed in previous papers are described. 1. Results of the analysis of DMCs light curves Pardo & Poretti (1997) determined the frequency content of Double–Mode Ce-pheids (DMCs) on the basis of the available V photometry; moreover, the Fourier decomposition was applied and very accurate sets of Fourier parameters were derived. In a second paper, Poretti & Pardo (1997a) discussed their properties by means of generalized phase differences. The main conclusions of the two papers were: 1. Each DMC displays a different content of harmonics and cross–coupling terms 2. The light curves of Classical Cepheids have the same Fourier parameters as the Fundamental (F) mode of DMCs 3. The light curves of s–Cepheids have the same Fourier parameters as the First Overtone (1O) Mode of DMCs 4. The discontinuity at P =3 d is observed also in the progression of the Fourier parameters of 1O DMC light curves 5. The light curve of the unique Second Overtone (2O) pulsator CO Aur is found to be perfectly sine–shaped (see also Poretti & Pardo 1997b) 6. No significant third periodicity was found 7. Only the F –mode of U TrA shows some hints of period variation 8. Only the 1O–mode of EW Sct shows some hints of amplitude variation 9. Generalized phase differences have well defined loci in the Fourier space parameters 1