  The study of Type Ia supernovae (SNIa) has lead to greatly improved insights
into many fields in astrophysics, however a theoretical explanation of the
origin of these events is still lacking. We investigate the potential
contribution to the SNIa rate from the population of merging double
carbon-oxygen white dwarfs. We aim to develope a model that fits the observed
SNIa progenitors as well as the observed close double white dwarf population.
We differentiate between two scenarios for the common envelope (CE) evolution;
the alpha-formalism based on the energy equation and the gamma-formalism that
is based on the angular momentum equation. In one model we apply the
alpha-formalism always. In the second model the gamma-formalism is applied,
unless the binary contains a compact object or the CE is triggered by a tidal
instability for which the alpha-formalism is used. The binary population
synthesis code SeBa was used to evolve binary systems from the zero-age main
sequence to the formation of double white dwarfs and subsequent mergers. SeBa
has been thoroughly updated since the last publication of the content of the
code. The limited sample of observed double white dwarfs is better represented
by the simulated population using the gamma-formalism than the alpha-formalism.
For both CE formalisms, we find that although the morphology of the simulated
delay time distribution matches that of the observations within the errors, the
normalisation and time-integrated rate per stellar mass are a factor 7-12 lower
than observed. Furthermore, the characteristics of the simulated populations of
merging double carbon-oxygen white dwarfs are discussed and put in the context
of alternative SNIa models for merging double white dwarfs.
