The magnitude to the maximum is, in our convention, the magnitude of the supernova in the observational filter considered corresponding to the date of the maximum of luminosity in the filter B.
To determine a distance from luminosity, we compare fluxes or the close magnitudes of objects (which are used as standard) and distances. To make this comparison, it is essential to express fluxes or these magnitudes in an identical photometric system, i.e. in the same filter.
As we saw in chapter 2 , the cosmological expansion involves a spectral shift of the light of the supernova.
In particular, the observation in a given filter will correspond to an all the more blue part of the spectrum which the redshift is large.
In practice, the observation of a supernova to a redshift of 0.5 in the filter R corresponds grosso-modo to an observation in the filter B in the reference frame of the supernova.
We take as convention to bring all the measures to the same reference frame: that of the supernova.
Our observations were in general made in various filters, chosen to correspond to the filters B and V in the reference frame of the supernova. These filters correspond coarsely to the couples (R,I) and (I,Z) for the supernovæ to redshifts of 0.5 and 0.9.
In fact the K-corrections presented at chapter 2 make it possible to express our fluxes or magnitudes in this photometric system. We will see in the continuation how to apply them.