  Hot DQ white dwarfs constitute a new class of white dwarf stars, uncovered
recently within the framework of the SDSS project. Recently, three hot DQ white
dwarfs have been reported to exhibit photometric variability with periods
compatible with pulsation g-modes. Here, we present a nonadiabatic pulsation
analysis of the recently discovered carbon-rich hot DQ white dwarf stars. One
of our main aims is to test the convective-mixing picture for the origin of hot
DQs through the pulsational properties. Our study relies on the full
evolutionary models of hot DQ white dwarfs recently developed by Althaus et al.
(2009), that consistently cover the whole evolution from the born-again stage
to the white dwarf cooling track. Specifically, we present a stability analysis
of white dwarf models from stages before the blue edge of the DBV instability
strip until the domain of the hot DQ white dwarfs, including the transition DB
--> hot DQ white dwarf. We found that at evolutionary phases in which the
models are characterized by He-dominated atmospheres, they exhibit unstable
$g$-mode pulsations typical of DBV stars, and when the models become DQ white
dwarfs with carbon-dominated atmospheres, they continue being pulsationally
unstable with similar characteristics than DB models, and in agreement with the
periods detected in variable hot DQ white dwarfs. Our calculations provide
strong support to the convective-mixing picture for the formation of hot DQs.
In particular, our results point to the existence of pulsating DB white dwarfs
with very thin He-rich envelopes, which after passing the DBV instability strip
become variable hot DQ stars. The existence of these DB stars with very thin
envelopes could be investigated through asteroseismology.
