  The explosion mechanism associated with thermonuclear supernovae (SNIa) is
still a matter of debate. There is a wide agreement that high amounts of of
radioactive nuclei are produced during these events and they are expected to be
strong gamma-ray emitters. In the past, several authors have investigated the
use of this gamma-ray emission as a diagnostic tool. In this paper we have done
a complete study of the gamma-ray spectra associated with all the different
scenarios currently proposed. This includes detonation, delayed detonation,
deflagration and the off-center detonation. We have performed accurate
simulations for this complete set of models in order to determine the most
promising spectral features that could be used to discriminate among the
different models. Our study is not limited to qualitative arguments. Instead,
we have quantified the differences among the spectra and established distance
limits for their detection. The calculations have been performed considering
the best current response estimations of the SPI and IBIS instruments aboard
INTEGRAL in such a way that our results can be used as a guideline to evaluate
the capabilities of INTEGRAL in the study of type Ia supernovae. For the
purpose of completeness we have also investigated the nuclear excitation and
spallation reactions as a possible secondary source of gamma-rays present in
some supernova scenarios. We conclude that this mechanism can be neglected due
to its small contribution.
