Color–magnitude diagrams (left panels) of the synthetic population of carbon-oxygen white dwarfs (blue symbols) and of helium-core white dwarfs (red symbols) and the corresponding white-dwarf luminosity functions (right panels). The observational selection area in the color–magnitude diagram of Bedin et al. (2005) is also shown using thin lines. These boundaries in the color–magnitude exclude low-mass helium-core white dwarfs. The observational white-dwarf luminosity function of Bedin et al. (2008b), which was corrected for incompleteness, is shown using black squares. Each theoretical luminosity function corresponds to an average of 10⁴ Monte Carlo realizations. The vertical thin line marks the magnitude limit  ≃ 28.5^mag above which the completeness level of the photometry falls below 50%. The top panels correspond to the case in which f_He = 0.3 and f_bin = 0.0 are adopted, while for the bottom ones we adopted f_He = 0.3 and f_bin = 0.54. See the online edition of the journal for a color version of this figure.