Helium ignition in rotating magnetized CO white dwarfs leading to fast and faint rather than classical Type Ia supernovae

Context. Based mostly on stellar models that do not include rotation, CO white dwarfs that accrete helium at rates of about similar to 10(-8) M-circle dot/yr have been put forward as candidate progenitors for a number of transient astrophysical phenomena, including Type Ia supernovae and the peculiar and fainter Type Iax supernovae. Aims. Here we study the impact of accretion-induced spin-up including the subsequent magnetic field generation, angular momentum transport, and viscous heating on the white dwarf evolution up to the point of helium ignition. Methods. We resolve the structure of the helium accreting white dwarf models with a one-dimensional Langrangian hydrodynamic code, modified to include rotational and magnetic effects, in 315 model sequences adopting different mass-transfer rates (10(-8)-10(-7) M-circle dot/yr), and initial white dwarf masses (0.54 1.10 M-circle dot) and luminosities (0.01 1 L-circle dot). Results. We find magnetic angular momentum transport, which leads to quasi-solid-body rotation, profoundly impacts the evolution of the white dwarf models, and the helium ignition conditions. Our rotating lower mass (0.54 and 0.82 M-circle dot) models accrete up to 50% more mass up to ignition than the non-rotating case, while it is the opposite for our more massive models. Furthermore, we find that rotation leads to helium ignition densities that are up to ten times smaller, except for the lowest adopted initial white dwarf mass. Ignition densities on the order of 106 g/cm(3) are only found for the lowest accretion rates and for large amounts of accreted helium (greater than or similar to 0.4 M-circle dot). However, correspondingly massive donor stars would transfer mass at much higher rates. We therefore expect explosive He-shell burning to mostly occur as deflagrations and at (M) over dot > 2 x 10(-8) M-circle dot/yr, regardless of white dwarf mass. Conclusions. Our results imply that helium accretion onto CO white dwarfs at the considered rates is unlikely to lead to the explosion of the CO core or to classical Type Ia supernovae, but may instead produce events that belong to the recently identified classes of faint and fast hydrogen-free supernovae.