CARBON SHELL OR CORE IGNITIONS IN WHITE DWARFS ACCRETING FROM HELIUM STARS

White dwarfs accreting from helium stars can stably burn at the accreted rate and avoid the challenge of mass loss associated with unstable helium burning that is a concern for many SNe Ia scenarios. We study binaries with helium stars of mass 1.25M(circle dot) <= M-He <= 1.8M(circle dot), which have lost their hydrogen rich envelopes in an earlier common envelope event and now orbit with periods (P-orb) of several hours with non-rotating 0.84 and 1.0M(circle dot) C/O WDs. The helium stars fill their Roche lobes after exhaustion of central helium and donate helium on their thermal timescales (similar to 10(5) years). As shown by others, these mass transfer rates coincide with the steady helium burning range for WDs, and grow the WD core up to near the Chandrasekhar mass (M-Ch) and a core carbon ignition. We show here, however, that many of these scenarios lead to an ignition of hot carbon ashes near the outer edge of the WD and an inward going carbon flame that does not cause an explosive outcome. For P-orb = 3 hr, 1.0M(circle dot) C/O WDs with donor masses M-He greater than or similar to 1.8M(circle dot). experience a shell carbon ignition, while M-He less than or similar to 1.3M(circle dot) will fall below the steady helium burning range and undergo helium flashes before reaching core C ignition. Those with 1.3M(circle dot) less than or similar to M-He less than or similar to 1.7M(circle dot) will experience a core C ignition. We also calculate the retention fraction of accreted helium when the accretion rate leads to recurrent weak helium flashes.