Double-Overtone Cepheids in the Large Magellanic Cloud

One of the most interesting results from the OGLE-III study of the LMC Cepheids is the large number of objects that pulsate simultaneously in the first and second overtone (denoted 1O/2O). Double-mode Cepheids yield important constraint on stellar evolution models. We show that great majority of the LMC 1O/2O Cepheids have masses M=3.0±0.5 Msolar. According to current stellar evolution calculations these masses are lower than needed for the blue loop in the helium burning phase to reach the instability strip. On the other hand, we found most of these stars significantly overluminous if they are crossing the instability strip before helium ignition. A possible solution of this discrepancy is to allow for a large overshooting from the convective core in the main sequence phase. We also discuss origin of double-mode pulsation. At the short period range we find two types of resonances that are conducive to this form of pulsation. However, at longer periods, it has a different (non-resonant) origin.