  We present a study exploring a systematic effect on the brightness of type Ia
supernovae using numerical models that assume the single-degenerate paradigm.
Our investigation varied the central density of the progenitor white dwarf at
flame ignition, and considered its impact on the explosion yield, particularly
the production and distribution of radioactive Ni-56, which powers the light
curve. We performed a suite of two-dimensional simulations with randomized
initial conditions, allowing us to characterize the statistical trends that we
present. The simulations indicate that production of Fe-group material is
statistically independent of progenitor central density, but the mass of stable
Fe-group isotopes is tightly correlated with central density, with a decrease
in the production of Ni-56 at higher central densities. These results imply
progenitors with higher central densities produce dimmer events. We provide
details of the post-explosion distribution of Ni-56 in the models, including
the lack of a consistent centrally-located deficit of Ni-56, which may be
compared to observed remnants. By performing a self-consistent extrapolation of
our model yields and considering the main-sequence lifetime of the progenitor
star and the elapsed time between the formation of the white dwarf and the
onset of accretion, we develop a brightness-age relation that improves our
prediction of the expected trend for single degenerates and we compare this
relation with observations.
