tokens: no selection criteria are employed – dashed line and open squares – and the luminosity function obtained when the selection criteria previously described are used – solid line and filled squares. It is worthwhile mentioning here that the theoretical luminosity functions have been normalized to the bin of bolometric magnitude , which corresponds to the magnitude bin for which the observed white dwarf luminosity function has the smallest error bars. Thus, since this luminosity bin is very close to the maximum of the luminosity function, the normalization criterion is practically equivalent to a number density normalization. As clearly seen in this figure, the theoretical results match very well the observed data, except for a quite apparent excess of hot white dwarfs, which is discussed in detail below. We note as well that the selection criteria employed by Limoges et al. (2015) basically affect the low luminosity tail of the white dwarf luminosity function, but not the location of the observed drop-off in the white dwarf number counts, nor that of the maximum of the luminosity function. This can be more easily seen by looking at the bottom panel of Fig. 2 , where the completeness of the simulated restricted sample is shown. We found that the completeness of the entire sample is . However, the restricted sample is nearly complete at intermediate bolometric magnitudes – between and 15 – but decreases very rapidly for magnitudes larger than , a clear effect of the selection procedure employed by Limoges et al. (2015) . Nevertheless, this low-luminosity tail is populated preferentially by helium-atmosphere stars and by very massive oxygen-neon white dwarfs. The prevalence of helium-atmosphere white dwarfs at low luminosities is due to the fact that stars with hydrogen-deficient atmospheres have lower luminosities than their hydrogen-rich counterparts of the same mass and age, because in their atmospheres collision-induced absorption does not play a significant role and cool to a very good approximation as black bodies. Also, the presence of massive oxygen-neon white dwarfs is a consequence of their enhanced cooling rate, owing to their smaller heat capacity. Fig. 3 Top panel : probability test as a function of the age obtained by fitting the three faintest bins defining the cut-off of the white dwarf luminosity function. Bottom panel : white dwarf luminosity function for the best-fit age. Fig. 4 Top panel : probability test as a function of the age of the burst of star formation obtained by fitting the nine brightest bins of the white dwarf luminosity function. Bottom panel : synthetic white dwarf luminosity function for a disk age of Gyr and a recent burst of star formation (black line), compared with the observed white dwarf luminosity function of (red lines). 4.2. Fitting the age Now we estimate the age of the disk using the standard method of fitting the position of the cut-off of the white dwarf luminosity function. We did this by comparing
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