  The progenitors of Type Ia supernovae (SNe Ia) have not been identified.
Though they are no longer fashionable we investigate the consequences if a
significant number of SNe Ia were edge-lit detonations (ELDs) of carbon/oxygen
white dwarfs that have accreted a critical mass of helium. Our best
understanding of the Phillips relation between light curve speed and peak
luminosity assigns both these phenomena to the amount of $^{56}$Ni produced. In
ELDs there are two sites of $^{56}$Ni synthesis. If the peak luminosity is
determined primarily by the C/O ratio in the core it is primarily a function of
its progenitor's initial mass. If the light curve decay speed is determined by
the total mass of iron group elements ejected this is a function of the total
mass of the ELD at the time of explosion. In general these two masses are
correlated and an empirical relation between peak luminosity and light curve
shape can be expected. However when we perform population synthesis for
progenitors of different metallicities we find a systematic shift in this
relation that would make distant SNe Ia fainter than those nearby. The
abundances of alpha-rich isotopes, such as $^{44}$Ca, in the solar system
indicate that only about 40 per cent of SNe Ia are edge-lit so any systematic
effect that could be present would be correspondingly diluted. If we examine
only the small subset of ELDs that accrete from a naked helium star, rather
than a He white dwarf, the systematic effect disappears.
