Why is there a Phillips relation? I want to know the explanation of Phillips relation, the relation seen in type Ia supernovae(SN Ia with broader light curve is brighter). More Ni-56 implies a larger luminosity at peak but what about broader light curve?
Check this paper: http://adsabs.harvard.edu/abs/2001ASPC..229..287M

LargerNi-56 directly implies brighter at peak, since it is the dominant source of radiation energy at early times.

The broadness of a light curve depends on the light curve timescale, which depends on ejecta mass, opacity, and kinetic energy. Since SNe Ia are from WD progenitors, there are not much different in ejecta mass. From simulations, kinetic energy is roughly the same across broad parameters. This leaves opacity to be the origin of the broadness. Since Fe-group elements have higher opacity than intermediate mass elements (IME), and more Ni-56 implies more Fe-group/IME, it is to be expected that high Ni-56 implies high opacity that implies broader light curve.

The slide, that someone provided in your comment, explains the same idea here (with more references).