The conditions at which an accreting carbon-oxygen white dwarf (CO WD) ignites C explosively have been considered to be possibly responsible for the maximum luminosity of Type Ia supernovae (SNe Ia). However, the exact conditions for this explosion have been in controversy. Employing the latest powerful stellar evolution code, Modules for Experiments in Stellar Astrophysics, and the descriptions of the single-degenerate (SD) model for progenitors of SNe Ia, we studied the evolution of several Pop I CO WDs from the onset of mass accretion to the explosive C ignition, where the temperature increases sharply but the density keeps in constant at the maximum temperature point (T-max) of the accreting CO WD. The accreted material is CO-rich and we include two sets of calculations, i.e. one is for a simple accretion like in Lesaffre et al. (2006) while the other artificially adds an energy generation rate (1 x 10(5) erg g(-1) s(-1)) in the outermost 0.005 M-circle dot material during accretion to mimic the energy delivered inwards from H- and He-burning. Both simulations show that most CO WDs ignite C explosively (at the T-max) in the centre, with very similar properties such as WD masses (similar to 1.387 M-circle dot), central densities (similar to 2.63 x 10(9) g cm(-3)), central temperatures(similar to 10(9) K) and binding energies (similar to 5.23 x 10(50) erg). This means that most SNe Ia are ignited initially in the centre of CO WDs based on the SD model. However, the central density and WD mass have been influenced by the initial C/O ratio at the centre of CO WDs. A few initially very cold massive CO WDs ignite C at off-centre points but still in the deep interior of WDs. In these explosions, the offset distance to the centre, the WD mass and central density at the explosion clearly increase with the cooling age, while the inclusion of an extra energy source resists this increasing in part. The off-centre explosions can only occasionally happen in relatively old galaxies and could partly contribute to the diversity of SNe Ia.
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