On the fraction of intermediate-mass close binaries that explode as Type Ia supernovae

Type Ia supernova (SNIa) explosions are thought to result from a thermonuclear runaway in CO white dwarfs (WDs) that approach the Chandrasekhar limit, either through accretion from a companion or through a merger with another WD. However, it is unknown which of these channels operates in reality, and what are the details of the process. I compile from the literature observational estimates of the fraction η of intermediate-mass stars that eventually explode as SNeIa, supplement them with several new estimates, and compare them self-consistently. The estimates are based on five different methods, each utilizing some observable related to the SNIa rate, combined with assumptions regarding the initial mass function (IMF): the ratio of SNIa to core-collapse explosions in star-forming galaxies; the SNIa rate per unit star formation rate; the SNIa rate per unit stellar mass; the iron-to-stellar mass ratio in galaxy clusters; and the abundance ratios in galaxy clusters. The five methods indicate that a fraction in the range η ~ 2-40 per cent of all stars with initial masses of 3-8M_solar (the progenitors of the WDs generally thought capable of exploding through the above scenarios) explode as SNeIa. A fraction of η ~ 15 per cent is consistent with all five methods for a range of plausible IMFs. Considering also the binarity fraction among such stars, the fraction of binaries with the appropriate mass ratios, the fraction in close initial orbits, and duplicity (every binary can produce only one SNIa explosion), this implies that nearly every intermediate-mass close binary ends up as an SNIa, or possibly more SNeIa than progenitor systems. Theoretically expected fractions are generally one to two orders of magnitude lower. The problem could be solved if all the observational estimates are in error, or with a `middle-heavy' IMF, or by some mechanism that strongly enhances the efficiency of binary evolution towards SNIa explosion, or by a non-binary origin for SNeIa.