  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.
