  The ultimate understanding of Type Ia Supernovae diversity is one of the most
urgent issues to exploit thermonuclear explosions of accreted White Dwarfs
(WDs) as cosmological yardsticks. In particular, we investigate the impact of
the progenitor system metallicity on the physical and chemical properties of
the WD at the explosion epoch. We analyze the evolution of CO WDs through the
accretion and simmering phases by using evolutionary models based on
time-dependent convective mixing and an extended nuclear network including the
most important electron captures, beta decays and URCA processes. We find that,
due to URCA processes and electron-captures, the neutron excess and density at
which the thermal runaway occurs are substantially larger than previously
claimed. Moreover, we find that the higher the progenitor metallicity, the
larger the neutron excess variation during the accretion and simmering phases
and the higher the central density and the convective velocity at the
explosion. Hence, the simmering phase acts as an amplifier of the differences
existing in SNe Ia progenitors. When applying our results to the neutron excess
estimated for the Tycho and Kepler young Supernova remnants, we derive that the
metallicity of the progenitors should be in the range Z=0.030-0.032, close to
the average metallicity value of the thin disk of the Milky Way. As the amount
of ${^{56}}$Ni produced in the explosion depends on the neutron excess and
central density at the thermal runaway, our results suggest that the light
curve properties depend on the progenitor metallicity.
