The galactic double-mode Cepheids I. Frequency analysis of the light curves and comparison with single-mode Cepheids

We submitted the available photometric V data of all the known galactic Double Mode Cepheids (DMCs) to a careful frequency analysis with the aim of detecting in each case the importance of the harmonics and of the cross coupling terms. For each object, starting from different data subsets, we progressively built a homogenous set of data, checking the consistency of the results step by step. It was demonstrated that each star displays a different content, showing that no a priori fit can be applied. Up to 4 harmonics were found for the fundamental radial mode (F); in every case, 2 harmonics were found for the first overtone radial mode (1 O). We also proceeded to a preliminar analysis of the Fourier parameters of the DMC light curves and we found a very close similarity between i) the light curves of the Classical Cepheids and those of the F-mode of the DMCs; ii) the light curves of the s-Cepheids and those of the 1 O-mode of the DMCs. The analysis of DMC light curves offers the possibility of unifying the light curves of Classical and s-Cepheids. The case of the unique DMC CO Aur is also discussed.