Type Ia supernovae (SNe Ia) are manifestations of stars deficient of hydrogen and helium disrupting in a thermonuclear runaway. While explosions of carbon-oxygen white dwarfs are thought to account for the majority of events, part of the observed diversity may be due to varied progenitor channels. We demonstrate that helium stars with masses between $sim$1.8 and 2.5 M$_{odot}$ may evolve into highly degenerate, near-Chandrasekhar mass cores with helium-free envelopes that subsequently ignite carbon and oxygen explosively at densities $sim(1.8-5.9)times 10^{9}$g cm$^{-3}$. This happens either due to core growth from shell burning (when the core has a hybrid CO/NeO composition), or following ignition of residual carbon triggered by exothermic electron captures on $^{24}$Mg (for a NeOMg-dominated composition). We argue that the resulting thermonuclear runaways is likely to prevent core collapse, leading to the complete disruption of the star. The available nuclear energy at the onset of explosive oxygen burning suffices to create ejecta with a kinetic energy of $sim$10$^{51}$ erg, as in typical SNe Ia. Conversely, if these runaways result in partial disruptions, the corresponding transients would resemble SN Iax events similar to SN 2002cx. If helium stars in this mass range indeed explode as SNe Ia, then the frequency of events would be comparable to the observed SN Ib/c rates, thereby sufficing to account for the majority of SNe Ia in star-forming galaxies.
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