HE STARS AND HE-ACCRETING CO WHITE-DWARFS

He star models in the mass range 0.4-1.0 M. have been evolved until the red giant phase or, depending on their mass, until crystallization on the white dwarf cooling sequence. Some of the degenerate structures obtained in these computations have been successively accreted at various He accretion rates in order to better define the fate of the accreting dwarf versus its mass and accretion rate for a fixed degeneracy level of the accreting dwarf (i.e., weak or strong degenerate He shell flash ignition or cooling down). He stars have been further induced to transfer mass to a degenerate companion through Roche lobe overflow, in conditions of large gravitational wave radiation (GWR) by the system. This to verify if the conditions necessary to obtain a strong, supernova-like, He flash are attained in the accreting CO dwarf. Physical parameters for this experiment are those estimated to occur in "real" systems and have been derived by an analysis of an appropriate population of progenitor binary systems, evolving through common envelope episodes. Our finding is that CO dwarfs, in binary systems with He stars, experience, as consequence of He accretion, a thermal behavior whose effects are such to locate the structure on the verge of obtaining a strong (supernova-like) explosive event. However, the models lie in a zone of the parameters space which is near to the border of the weak flashes zone; as a consequence our results cannot firmly support that in nature, very close binary systems of He stars and CO dwarfs, can indeed be the progenitors of some subtype of the Type I class of supernovae. We find, however, that if these systems do indeed develop a supernova explosion, such supernovae would produce rather homogeneous light curves and spectral evolutions.