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The white dwarf cooling sequence of 47 Tucanae

47 Tucanae is one of the most interesting and well observed and theoretically studied globular clusters. This allows us to study the reliability of our understanding of white dwarf cooling sequences, to confront different methods to determine its age, and to assess other important characteristics, like its star formation history. Here we present a population synthesis study of the cooling sequence of the globular cluster 47 Tucanae. In particular, we study the distribution of effective temperatures, the shape of the color-magnitude diagram, and the corresponding magnitude and color distributions. We do so using an up-to-date population synthesis code based on Monte Carlo techniques, that incorporates the most recent and reliable cooling sequences and an accurate modeling of the observational biases. We find a good agreement between our theoretical models and the observed data. Thus, our study, rules out previous claims that there are still missing physics in the white dwarf cooling models at moderately high effective temperatures. We also derive the age of the cluster using the termination of the cooling sequence, obtaining a good agreement with the age determinations using the main-sequence turn-off. Finally, we find that the star formation history of the cluster is compatible with that btained using main sequence stars, which predict the existence of two distinct populations. We conclude that a correct modeling of the white dwarf population of globular clusters, used in combination with the number counts of main sequence stars provides an unique tool to model the properties of globular clusters.