The type Ia supernova width-luminosity relation

Observations of type Ia supernovæ at high redshifts have become an important tool for studying the geometry of the universe. The relation between the duration of the peak phase of a type Ia supernova's lightcurve and its luminosity (broader is brighter) forms the cornerstone of this measurement, yet it is a purely empirical relation. In this paper we show that the relation is a natural consequence of the radiation transport in type Ia supernovae and suggest constraints on the nature of the explosions which arise from our interpretation of the observed relation. The principle parameter underlying the relation is the mass of radioactive ⁵⁶Ni produced in the explosion. The relation is shown to be relatively insensitive to most other parameters in Chandrasekhar-mass explosions. Cosmological results are thus unlikely to suffer from systematic effects stemming from evolution in the explosions' progenitors.