Testing the initial-final mass relationship of white dwarfs

In this contribution we revisit the initial-final mass relationship of white dwarfs, which links the mass of a white dwarf with that of its progenitor in the main-sequence. Although this function is of paramount importance to several fields in modern astrophysics, it is still not well constrained either from the theoretical or the observational points of view. We present here a revision of the present semi-empirical initial-final mass relationship using all the available data and including our recent results obtained from studying white dwarfs in common proper motion pairs. We have also analyzed the results obtained so far to provide some clues on the dependence of this relationship on metallicity. Finally, we have also performed an indirect test of the initial-final mass relationship by studying its effect on the luminosity function and on the mass distribution of white dwarfs.