Type Ia supernovae have two physical width-luminosity relations and they favor sub-Chandrasekhar and direct collision models - II. Color evolution

While the width-luminosity relation (WLR) among type Ia supernovae (slower is brighter) is one of the best studied properties of this type of events, its physical basis has not been identified convincingly. The 'luminosity' is known to be related to a clear physical quantity -- the amount of $^{56}$Ni synthesized, but the 'width' has not been quantitatively linked yet to a physical time scale. We show that the recombination time of $^{56}$Fe and $^{56}$Co from doubly to singly ionized states causes the typical observed break in the color curve B-V due to a cliff in the mean opacities, and is a robust width measure of the light curve, which is insensitive to radiation transfer uncertainties. A simple photospheric model is shown to predict the recombination time to an accuracy of $\sim5$ days, allowing a quantitative understanding of the color WLR. Two physical times scales of the width luminosity relation are shown to be set by two column densities -- the total column density which sets the gamma-ray escape time $t_0$ (previous Paper I) and the $^{56}$Ni column density which sets the recombination time (this Paper II). Central detonations of sub-$\rm M_{ch}$ WDs and direct WD collision models have gamma-ray escape times and recombination times which are consistent with observations across the luminosity range of type Ia's. Delayed detonation Chandrasekhar mass models have recombination times that are broadly consistent with observations, with tension at the bright end of the luminosity range and inconsistent gamma-ray escape times at the faint end.