  We perform an analysis of the single white dwarf and the double degenerate
binary populations in the solar neighbourhood following a population synthesis
approach to investigate the effects of unresolved double degenerates in the
white dwarf luminosity function. We consider all unresolved synthetic binaries
to be associated with fictitious effective temperatures and surface gravities
that are obtained in the same way as if these objects were observed as single
point sources. We evaluate the effects of unresolved double white dwarfs
assuming that the synthetic samples are observed both by the magnitude-limited
SDSS and the volume-limited Gaia surveys, the latter limited to a distance of
no more than 100pc. We find that, for our standard model, the impact of
unresolved double degenerates in the white dwarf luminosity function derived
from the Gaia sample is nearly negligible. Unresolved double degenerates are
hence expected to have no effect on the age of the Galactic disc, nor on the
star formation history from this population. However, for the SDSS sample, the
effect of unresolved double degenerates is significant at the brighter bins
(Mbol<6.5 mag), with the fraction of such systems reaching ~40% of the total
white dwarf population at Mbol=6 mag. This indicates unresolved double
degenerates may influence the constraints on the star formation history derived
from the SDSS white dwarf sample.
