On the Origin of the Type Ia Supernova Width-Luminosity Relation
  Brighter Type Ia supernovae (SNe Ia) have broader, more slowly declining B-band light curves than dimmer SNe Ia. We study the physical origin of this width-luminosity relation (WLR) using detailed radiative transfer calculations of Chandrasekhar mass SN Ia models. We find that the luminosity dependence of the diffusion time (emphasized in previous studies) is in fact of secondary relevance in understanding the model WLR. Instead, the essential physics involves the luminosity dependence of the spectroscopic/color evolution of SNe Ia. Following maximum-light, the SN colors are increasingly affected by the development of numerous Fe II/Co II lines which blanket the B-band and, at the same time, increase the emissivity at longer wavelengths. Because dimmer SNe Ia are generally cooler, they experience an earlier onset of Fe III to Fe II recombination in the iron-group rich layers of ejecta, resulting in a more rapid evolution of the SN colors to the red. The faster B-band decline rate of dimmer SNe Ia thus reflects their faster ionization evolution. 
Daniel Kasen and S.E. Woosley