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Single-Degenerate Type Ia Supernovae Are Preferentially Overluminous

Recent observational and theoretical progress has favored merging and helium-accreting sub-Chandrasekhar mass white dwarfs in the double-degenerate and the double-detonation channels, respectively, as the most promising progenitors of normal Type Ia supernovae (SNe Ia). Thus the fate of rapidly-accreting Chandrasekhar mass white dwarfs in the single-degenerate channel remains more mysterious then ever. In this paper, we clarify the nature of ignition in Chandrasekhar-mass single-degenerate SNe Ia by analytically deriving the existence of a characteristic length scale which establishes a transition from central ignitions to buoyancy-driven ignitions. Using this criterion, combined with data from three-dimensional simulations of convection and ignition, we demonstrate that the overwhelming majority of ignition events within Chandrasekhar-mass white dwarfs in the single-degenerate channel are buoyancy-driven, and consequently lack a vigorous deflagration phase. We thus infer that single-degenerate SNe Ia are generally expected to lead to overluminous 1991T-like SNe Ia events. We establish that the rates predicted from both the population of supersoft X-ray sources and binary population synthesis models of the single-degenerate channel are broadly consistent with the observed rates of overluminous SNe Ia, and suggest that the population of supersoft X-ray sources are the dominant stellar progenitors of SNe 1991T-like events. We further demonstrate that the single-degenerate channel contribution to the normal and failed 2002cx-like rates is not likely to exceed 1% of the total SNe Ia rate. We conclude with a range of observational tests of overluminous SNe Ia which will either support or strongly constrain the single-degenerate scenario.