  Two formation scenarios are investigated for type Ia supernovae in elliptical
galaxies: the single degenerate scenario (a white dwarf reaching the
Chandrasekhar limit through accretion of matter transferred from its companion
star in a binary) and the double degenerate scenario (the inspiraling and
merging of two white dwarfs in a binary as a result of the emission of
gravitational wave radiation). A population number synthesis code is used,
which includes the latest physical results in binary evolution and allows to
differentiate between certain physical scenarios (such as the description of
common envelope evolution) and evolutionary parameters (such as the mass
transfer efficiency during Roche lobe overflow). The thus obtained theoretical
distributions of type Ia supernova delay times are compared to those that are
observed, both in morphological shape and absolute number of events. The
critical influence of certain parameters on these distributions is used to
constrain their values. The single degenerate scenario alone is found to be
unable in reproducing the morphological shape of the observational delay time
distribution, while use of the double degenerate one (or a combination of both)
does result in fair agreement. Most double degenerate type Ia supernovae are
formed through a normal, quasi-conservative Roche lobe overflow followed by a
common envelope phase, not through two successive common envelope phases as is
often assumed. This may cast doubt on the determination of delay times by using
analytical formalisms, as is sometimes done in other studies. The theoretical
absolute number of events in old elliptical galaxies lies a factor of at least
three below the rates that are observed. While this may simply be the result of
observational uncertainties, a better treatment of the effects of rotation on
stellar structure could mitigate the discrepancy.
