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White dwarfs accreting from helium stars can stably burn at the accreted rateand avoid the challenge of mass loss associated with unstable Helium burningthat is a concern for many Type Ia supernovae scenarios. We study binaries withhelium stars of mass $1.25 M_\odot\le M_{\rm{He}} \le 1.8 M_\odot$, which havelost their hydrogen rich envelopes in an earlier common envelope event and noworbit with periods ($P_{\rm orb}$) of several hours with non-rotating $0.84$and $1.0 M_\odot$ C/O WDs. The helium stars fill their Roche lobes (RLs) afterexhaustion of central helium and donate helium on their thermal timescales(${\sim}10^5$yr). As shown by others, these mass transfer rates coincide withthe steady helium burning range for WDs, and grow the WD core up to near theChandrasekhar mass ($M_{\rm Ch}$) and a core carbon ignition. We show here,however, that many of these scenarios lead to an ignition of hot carbon ashesnear the outer edge of the WD and an inward going carbon flame that does notcause an explosive outcome. For $P_{\rm orb} = 3$ hours, $1.0 M_\odot$ C/O WDswith donor masses $M_{\rm He}\gtrsim1.8 M_\odot$ experience a shell carbonignition, while $M_{\rm He}\lesssim1.3 M_\odot$ will fall below the steadyhelium burning range and undergo helium flashes before reaching core Cignition. Those with $1.3 M_\odot \lesssim M_{\rm He} \lesssim 1.7 M_\odot$will experience a core C ignition. We also calculate the retention fraction ofaccreted helium when the accretion rate leads to recurrent weak helium flashes.

Carbon Shell or Core Ignitions in White Dwarfs Accreting from Helium Stars