Constraints on the models

To be realistic, a model of explosion must reproduce a certain number of observational characteristics:

1. The composition of ejecta and the particular speeds observed in the spectra and the lightcurves. In particular, the explosion must be sufficiently powerful (it must produce Ni ${ }^{56}$sufficient) and produce sufficient elements of intermediate mass high speed in the external layers. Moreover, isotopic abundances should not be very different from those observed in the solar system.

2. The process of explosion must be robust in order to reproduce the homogeneity of the supernovæ Ia communes; the models should not be very dependent on the parameters of the explosion or the initial conditions.

3. The models must be able to reproduce the intrinsic variations observed in the luminosities. If the basic models must be robust with small variations, it must exist at least a parameter which accounts for the dispersion of the power of the explosion.

4. The power of the explosion must be dependent causalement with the state in which was the dwarf white one before the explosion in order to account for the variations observed according to the stellar population of the galaxy host.