Type I (absence of hydrogen lines) SN observed NEARBY show a relationship between PEAK LUMINOSITY and TIMESCALE of their light curve
brighter SN are slower - fainter are faster
SN Ia are not all the same. Variations occur in their light curves and spectra. We use the “stretch” parameter to correct for these differences in the distance measurements. The following observations show the entire range in SN Ia brightness.
Simple linear relation between absolute magnitude and a ‘stretch factor’ multiplying the light curve timescale fits the data well.
Lower plot shows the NEARBY SN from the upper plot after fitting and removing the stretch factor and correcting peak magnitude .. this is a straightforward calibration.
After K-correcting (for time-dilation) using the redshift, variations in SNe Ia light curves can be “corrected” so their peak brightness can be used to measure distance (time) to the supernova.