, corrections MLCS or the factor of stretching. As we saw, there is a correlation between the luminosity to the maximum and the width of the lightcurve. To measure this width makes it possible to devaluate the luminosity of the supernova to improve the estimator of distance.
There are several empirical descriptions of this correlation width-luminosity (see chapter 6 ): the measurement of , corrections MLCS or the factor of stretching.
Our goal is to simulate the lightcurves directly in the system of observation of the supernovæ. In particular, we want to have a model which can reproduce all the types of lightcurves by using continuous parameters.
goldhaber2001 showed that the factor of stretching was able to reproduce the diversity of the curves of light used during the cosmological estimates of parameters (perlmutter1999).
The principal disadvantage of this method is that it does not make it possible to reproduce correctly the lightcurves more than one about thirty day after the maximum of luminosity out of B Cependant, the supernovæ with great shifts towards the red are in general observed during 2 to 3 months, that is to say between 40 and 60 days in the reference frame of a supernova to a shift towards the red of 0.5, the observations are in general begun before the maximum of luminosity, the observations thus corresponding in general to the period over which, this approach functions. Let us recall that the principle of this model is to adjust the time scale of a single owner of lightcurve to describe the variations rate of noted rise and decrease.
We will thus use this method by restricting us the analysis of the lightcurves at the period going 15 days before the maximum (the lightcurves are very badly known before), up to 35 days after the maximum in the reference frame of the supernova.