6 Conclusions

We have used the OGLE data base and Kurucz atmosphere models to obtain periods, effective temperatures and luminosities for fundamental and overtone Magellanic Cloud Cepheids. With an assumed average composition of (X=0.716, Z=0.010) for the LMC and of (X=0.726, Z=0.004) for the SMC, stellar masses have been computed with the Florida pulsation code for the observationally derived P, L and $T_{\rm {ef f}}$. The best results are obtained by adopting the "long'' distances to the clouds. Reddening maps, as opposed to average MC reddenings, do not reduce the unexpectedly large scatter in M-L, and we conclude that individual stellar reddenings would be necessary. However, the largest source of the scatter is in the V and I photometric errors. The M-L relations for the fundamental and for the first overtone Cepheids match closely for each Magellanic Cloud. Both the SMC and the LMC ${{\rm Log}}\, M$- ${{\rm Log}}\, L$relations have a noticeable curvature.

A comparison with the predictions of the recent stellar evolution calculations show a discrepancy in the M-L diagrams, where the evolutionary tracks are underluminous. It also confirms a discrepancy in the theoretical HR diagrams, especially for the SMC, where the low mass tracks do not extend sufficiently blue-ward to penetrate the instability strip. Our M-L relations are useful as a new type of constraint that the evolutionary tracks have to satisfy.

Acknowledgements

This work has been supported by the National Science Foundation (AST98-19608) and by the Hungarian OTKA (T-026031). It is based on observations coming from the public archive from the OGLE-II microlensing experiment. We have profited from a fruitful correspondence with Géza Kovács, Isabelle Baraffe, Marie-Jo Goupil, Daniel Cordier, Giuseppe Bono. We thank Andrejz Udalski for his comments on the paper. Two of us (JRB and ZK) gratefully acknowledge the hospitality of the Institut d'Astrophysique de Paris, as a "Professeur invité de l'Université Paris VI'' (JRB), and as a "Poste rouge'' (ZK).