When carbon is ignited off-center in a CO core of a super-AGB star, its burning in a convective shell tends to propagate to the center. Whether the C flame will actually be able to reach the center depends on the efficiency of extra mixing beneath the C convective shell. Whereas thermohaline mixing is too inefficient to interfere with the C-flame propagation, convective boundary mixing can prevent the C burning from reaching the center. As a result, a C-O-Ne white dwarf (WD) is formed, after the star has lost its envelope. Such a hybrid WD has a small CO core surrounded by a thick ONe zone. In our 1D stellar evolution computations the hybrid WD is allowed to accrete C-rich material, as if it were in a close binary system and accreted H-rich material from its companion with a sufficiently high rate at which the accreted H would be processed into He under stationary conditions, assuming that He could then be transformed into C. When the mass of the accreting WD approaches the Chandrasekhar limit, we find a series of convective Urca shell flashes associated with high abundances of 23Na and 25Mg. They are followed by off-center C ignition leading to convection that occupies almost the entire star. To model the Urca processes, we use the most recent well-resolved data for their reaction and neutrino-energy loss rates. Because of the emphasized uncertainty of the convective Urca process in our hybrid WD models of SN Ia progenitors, we consider a number of their potentially possible alternative instances for different mixing assumptions, all of which reach a phase of explosive C ignition, either off or in the center. Our hybrid SN Ia progenitor models have much lower C to O abundance ratios at the moment of the explosive C ignition than their pure CO counterparts, which may explain the observed diversity of the SNe Ia.
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