  We explore the hypothesis, that helium stars in a certain mass range can
evolve to a carbon core explosion similar to what is widely accepted as an
explanation for the SN I phenomenon. This should happen when their
carbon-oxygen core grows thanks to the helium shell burning above the core. We
found that in the mass range of about 1.7-2.2 Msun, indeed this can happen.
  The main new insight we believe we gained is the crucial importance of an
"early" off-center ignition of carbon, which at a later stage prevents the
carbon which forms below the helium burning shell and ignites, from burning the
carbon all the way to the center. When helium is almost depleted in the
convective envelope by the helium burning shell at its bottom, the now
super-Chandrasekhar mass carbon-oxygen core contracts, and the residual
degenerate carbon at the center is ignited, resulting in a runaway similar to
the classical SN I scenario.
  Since the structure and behavior of the carbon-oxygen core of the helium
stars of our interest is very similar to that of a mass accreting carbon-oxygen
star, we also thoroughly examined the behavior of carbon-oxygen stars. We
discovered that the models which ignite carbon off-center (in the mass range of
about 1.05-1.18 Msun, depending on the carbon mass fraction) present an
interesting SN I progenitor scenario of their own, since whereas in the
standard scenario runaway always takes place at the same density of about 2E9
gr/cm3, in our case, due to the small amount of carbon ignited, we get a whole
range of densities from 1E9 up to 6E9 gr/cm3.
