  An accurate assessment of white dwarf cooling times is paramount to place
white dwarf cosmochronology of Galactic populations on more solid grounds. This
issue is particularly relevant in view of the enhanced observational
capabilities provided by the next generation of Extremely Large Telescopes,
that will offer more avenues to employ white dwarfs as probes of Galactic
evolution and test-beds of fundamental physics. We estimate for the first time
the consistency of results obtained from two independent and widely used
evolutionary codes (BaSTI and LPCODE) for white dwarf models with fixed mass
and chemical stratification, when the same input physics is employed in both
codes. We considered 0.55Msun white dwarf models with both pure carbon and
uniform carbon-oxygen (50/50 mass fractions) core. We have assessed for the
first time the maximum possible accuracy in the current estimates of white
dwarf cooling times, resulting only from the different implementations of the
stellar evolution equations and homogeneous input physics in two independent
stellar evolution codes. This accuracy amounts to 2% at luminosities lower than
log(L/L_{\sun})= -1.5$. This agreement is true for both pure carbon and uniform
carbon-oxygen stratification core models, and also when the release of latent
heat and carbon-oxygen phase separation are considered. This difference is
smaller than the uncertainties in cooling times due to the present
uncertainties in the white dwarf chemical stratification. We have also
determined quantitatively and explained the effect of varying equation of
state, low-temperature radiative opacities and electron conduction opacities in
our calculation. Finally, we extend the scope of our work by providing
tabulations of our cooling sequences and the required input physics, that can
be used as a comparison test of cooling times obtained from other white dwarf
evolutionary codes.
