Latest generation white dwarf cooling models : theory and applications

White dwarfs are the most common stellar evolutionary end-point. Moreover, they can be considered as reliable cosmic clocks to infer the age of a wide variety of stellar populations, including globular and open clusters. Consequently, there is a considerable interest in the study of white dwarf cooling models. In this thesis we used two different approaches. From a theorical perspective, we computed a set of new cooling white dwarfs sequences which incorporates the most up-to-date physical inputs for precision white dwarf cosmochronology and for asteroseismological studies of ZZ Ceti stars. Moreover, we studied the role of 22Ne diffusion in the evolution of white dwarf stars with high-metallicity progenitors. Our evolutionary sequences have been self-consistently evolved from the zero age main sequence to the white dwarf stage. Our calculations include: nuclear burning at the very early phases of white dwarf evolution (which is important to determine the final thickness of the hydrogen-rich envelope), diffusion and gravitational settling (which are important to shape the profiles of the outer layers), accurate neutrino emission rates (which control the cooling at high luminosities), a correct treatment of crystallization and phase separation of carbon and oxygen (which dominate the cooling times at low luminosities), a very detailed equation of state (which is important in all the evolutionary phases), and improved non-gray model atmospheres (which allow for a precise determination of white dwarf colors and outer boundary conditions for the evolving models). From an applied point of view, we use a Monte Carlo simulator that employs our up-to-date evolutionary cooling sequences for white dwarfs. From this and the observations obtained by Hubble Space Telescope of NGC 6791, a nearby metal-rich open cluster, we obtain important conclusions. NGC 6791 is a well studied metal-rich open cluster ([Fe/H]¿ 0.4) that it is so close to us that can be imaged down to luminosities fainter than that of the termination of its white-dwarf cooling sequence, thus allowing for an in-depth study of its white dwarf population. We constrain important properties of this cluster stellar population, such as the age, or the existence of a putative population of massive helium core white dwarfs among other aspects. Some of our main findings can be summarized as follows. With respect to the computation of new cooling sequences for hydrogen-rich DA white dwarfs (Renedo et al. 2010) We correctly reproduced the observed initial-to-final mass relationship of white dwarfs with solar metallicity progenitors. We calculated the energy released from 22Ne sedimentation and we confirm this energy release strongly delays the cooling. The precise value of the delays depends on the mass of the white dwarf, its luminosity and on the metal content. We also solved the age discrepancy between the main sequence turn-off age (~ 8 Gyr) and the age derived from the termination of the white dwarf cooling sequence (~ 6 Gyr). Finally we found that the fraction of non-DA white dwarfs in this particular cluster is surprinsingly small, on the order of 6%.