Models for the evolution of close binaries with He-star and white dwarf components towards Type Ia supernova explosions

Context. Type Ia supernovae (SNe Ia) have been an important tool for astronomy for quite some time; however, the nature of their progenitors remains somewhat mysterious. Recent theoretical studies indicated the possibility of producing thermonuclear detonations of carbon-oxygen white dwarfs (CO WDs) at masses less than the Chandrasekhar mass through accretion of helium-rich matter, which would, depending on mass accretion rate, mass, and initial temperature of the WD, spectrally resemble either a normal SN Ia or a peculiar one. Aims. This study aims to further resolve the state of binary systems comprised of a sub-Chandrasekhar-mass CO WD and a helium star at the point where an accretion-induced detonation occurs and constrains the part of the initial parameter space where this kind of phenomenon is possible. Methods. Preexisting data obtained through simulations of single, constantly accreting CO WDs is used as an indicator for the behavior of new binary models in which the WD is treated as a point mass and which include the non-degenerate partner as a fully resolved stellar model. We parameterize the ignition of the accumulated helium layer, changes in the WD temperature, and changes in the CO core mass depending on the mass transfer rate. Results. The initial conditions allowing for detonation do not form a single contiguous area in the parameter space, whose shape is profoundly influenced by the behavior of the donor star. Mass loss due to Nova outbursts acts in favor of detonation. According to our criteria, about 10% of the detonations in this study can be expected to show spectra consistent with ordinary SNe Ia; the rest exhibit peculiar features