The effects of $^{22}$Ne sedimentation and metallicity on the local 40
  pc white dwarf luminosity function
  We analyze the effect of the sedimentation of $^{22}$Ne on the local white
dwarf luminosity function by studying scenarios under different Galactic
metallicity models. We make use of an up-to-date population synthesis code
based on Monte Carlo techniques to derive the synthetic luminosity function.
Constant solar metallicity models are not able to simultaneously reproduce the
peak and cut-off of the white dwarf luminosity function. The extra release of
energy due to $^{22}$Ne sedimentation piles up more objects in brighter bins of
the faint end of the luminosity function. The contribution of a single burst
thick disk population increases the number of stars in the magnitude interval
centered around $M_{\rm bol}=15.75$. Among the metallicity models studied, the
one following a Twarog's profile is disposable. Our best fit model was obtained
when a dispersion in metallicities around the solar metallicity value is
considered along with a $^{22}$Ne sedimentation model, a thick disk
contribution and an age of the thin disk of $8.8\pm0.2$ Gyr. Our population
synthesis model is able to reproduce the local white dwarf luminosity function
with a high degree of precision when a dispersion in metallicities around the
solar value model is adopted. Although the effects of $^{22}$Ne sedimentation
are 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 the
white dwarf luminosity function.
