Constraints on white dwarfs structure and evolution from asteroseismology

In the last two decades, considerable efforts have been devoted to the study of white dwarfs pulsators. Owing to ground-based multi-sites observational campaigns, and more recently to the long time-based high-precision photometric observations with the Kepler satellite, a large number of pulsating white dwarfs have been studied through the asteroseismology method. I emphasize here the accuracy that this method achieves on the determination of the total mass, one of the fundamental stellar parameter that can be derived from asteroseismology, among others. Then I discuss the issue of the age determination, emphasizing the contribution of the neutrinos cooling and the importance of the outer layer mass fraction. I show that some observations throw some doubts on the assumption that the cooling is the only cause of the observed frequency variations. Finally I summarize the results demonstrating that the entire stellar angular momentum is lost during the evolutionary phases prior to the white dwarf stage. While the asteroseismology of white dwarf stars has given a rich harvest of results on their internal structure and evolution, there are still some challenges to face. Determining accurate mass of the outer layers, specifically for the DA white dwarfs, is one of them. An increasing number of white dwarf pulsators are now known to exhibit frequency and amplitude temporal variations. The physical mechanism producing such variabilities has to be identified.