ABSTRACT
We review the candidate progenitor binary systems of Type Ia supernovae (SNe Ia). We argue that the exploding star is likely to be a mass accreting carbon-oxygen white dwarf. "Primary" characteristics of SNe Ia, such as the composition of the ejected matter as a function of the ejection velocity, depend on whether th efirst nuclear ignition takes place in carbon-oxygen at or near the center of a Chandrasekhar-mass white dwarf, or off-center, in a helium layer of a sub-Chandrasekhar white dwarf. The primary characteristics of SNe Ia, as inferred from observation, favor carbon ignitors rather than helium ignitors. "Secondary" characteristics of SNe Ia that are determined by the nature of the donor star and the accretion process tend to be environmental, i.e., having to do with a circumstellar medium. We consider seven candidate progenitor systems for carbon ignitors as well as four candidate systems for helium ignitors, and we discuss the feasibility of identifying the progenitor systems by means of observations of the secondary characteristics of SNe Ia. The most promising tests at present appear to be searches for radio emission, to constrain the circumstellar density, and for narrow lines of hydrogen, helium, carbon, and oxygen in early and late time spectra, to determine the composition of the donor star. We conclude with reasons for suspecting that the coalescence of pairs of C-O white dwarfs, and the accretion of hydgrogen on a thermal timescale via Roche lobe overflow from subgiant donors, are the two most promising candidate progenitors of SNe Ia.