We present a new set of cooling models and isochrones for both H- and He-atmosphere white dwarfs, incorporating accurate boundary conditions from detailed model atmosphere calculations, and carbon-oxygen chemical abundance profiles based on updated stellar evolution calculations from the BaSTI stellar evolution archive - a theoretical data center for the Virtual Observatory. We discuss and quantify the uncertainties in the cooling times predicted by the models, arising from the treatment of mixing during the central H- and He-burning phases, number of thermal pulses experienced by the progenitors, progenitor metallicity and the $^{12}C(alpha,gamma)^{16}O$ reaction rate. The largest sources of uncertainty turn out to be related to the treatment of convection during the last stages of the progenitor central He-burning phase, and the $^{12}C(alpha,gamma)^{16}O$ reaction rate. We compare our new models to previous calculations performed with the same stellar evolution code, and discuss their application to the estimate of the age of the solar neighborhood, and the interpretation of the observed number ratios between H- and He-atmosphere white dwarfs. The new white dwarf sequences and an extensive set of white dwarf isochrones that cover a large range of ages and progenitor metallicities are made publicly available at the official BaSTI website.
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