  Type-Ia supernovae (SNe-Ia) are thought to result from a thermonuclear
runaway in white dwarfs (WDs) that approach the Chandrasekhar limit, either
through accretion from a companion or a merger with another WD. I compile
observational estimates of the fraction eta of intermediate-mass stars that
eventually explode as SNe-Ia, supplement them with several new estimates, and
compare them self-consistently. The estimates are based on five different
methods, each utilising some observable related to the SN-Ia rate, combined
with assumptions regarding the IMF: the ratio of SN-Ia to core-collapse rates
in star-forming galaxies; the SN-Ia rate per unit star-formation rate; the
SN-Ia 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 eta~2-40% of all stars with initial
masses of 3-8 M_sun (the generally assumed SN-Ia progenitors) explode as
SNe-Ia. A fraction of eta~15% is consistent with all five methods for a range
of plausible IMFs. Considering also the binarity fraction among such stars, the
mass ratio distribution, the separation distribution, and duplicity (every
binary can produce only one SN-Ia explosion), this implies that nearly every
intermediate mass close binary ends up as a SN-Ia, or possibly more SNe-Ia 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 toward
SN-Ia explosion; or by a non-binary origin for SNe-Ia.

Astrophysics