Quantifying systematic uncertainties in white dwarf cooling age determinations

Cooling ages of white dwarfs are routinely determined by mapping effective temperatures and masses to ages using evolutionary models. Typically, the reported uncertainties on cooling ages only consider the error propagation of the uncertainties on the spectroscopically or photometrically determined $T_{\rm eff}$ and mass. However, cooling models are themselves uncertain, given their dependence on many poorly constrained inputs. This paper estimates these systematic model uncertainties. We use MESA to generate cooling sequences of $0.5-1.0 M_{\odot}$ hydrogen-atmosphere white dwarfs with carbon-oxygen cores under different assumptions regarding the chemical stratification of their core, the thickness of their helium envelope, their hydrogen content, and the conductive opacities employed in the calculations. The parameter space explored is constrained by the range of values predicted by a variety of stellar evolution models and inferred from asteroseismological studies. For a $0.6 M_{\odot}$ white dwarf, we find an uncertainty of 0.03 Gyr at 10,000 K (corresponding to a 5% relative uncertainty) and 0.8 Gyr at 4000 K (9%). This uncertainty is significant, as it is comparable to the age uncertainty obtained by propagating the measurement errors on $T_{\rm eff}$ and mass for a typical white dwarf. We also separately consider the potential impact of $^{22}$Ne shell distillation, which plausibly leads to an additional uncertainty of $\sim 1$ Gyr for crystallized white dwarfs. We provide a table of our simulation results that can be used to evaluate the systematic model uncertainty based on a white dwarf's $T_{\rm eff}$ and mass. We encourage its use in all future studies where white dwarf cooling ages are measured.