  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. 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. 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. 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.
