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We analyze the effect of the sedimentation of $^{22}$Ne on the local whitedwarf luminosity function by studying scenarios under different Galacticmetallicity models. We make use of an up-to-date population synthesis codebased on Monte Carlo techniques to derive the synthetic luminosity function.Constant solar metallicity models are not able to simultaneously reproduce thepeak and cut-off of the white dwarf luminosity function. The extra release ofenergy due to $^{22}$Ne sedimentation piles up more objects in brighter bins ofthe faint end of the luminosity function. The contribution of a single burstthick disk population increases the number of stars in the magnitude intervalcentered around $M_{\rm bol}=15.75$. Among the metallicity models studied, theone following a Twarog's profile is disposable. Our best fit model was obtainedwhen a dispersion in metallicities around the solar metallicity value isconsidered along with a $^{22}$Ne sedimentation model, a thick diskcontribution and an age of the thin disk of $8.8\pm0.2$ Gyr. Our populationsynthesis model is able to reproduce the local white dwarf luminosity functionwith a high degree of precision when a dispersion in metallicities around thesolar value model is adopted. Although the effects of $^{22}$Ne sedimentationare only marginal and the contribution of a thick disk population is minor,both of them help in better fitting the peak and the cut-off regions of thewhite dwarf luminosity function.

The effects of $^{22}$Ne sedimentation and metallicity on the local 40 pc white dwarf luminosity function