The present paper focuses on the evolution of hydrogen-deficient white dwarfs with the aim of exploring the consequences of different initial envelope structures on the carbon abundances expected in helium-rich, carbon-contaminated DQ white dwarfs. In particular, the evolutionary link between the DQs with low detected carbon abundances and the PG1159, extreme horizontal branch, and helium-rich R Coronae Borealis (RCrB) stars is explored. We present full evolutionary calculations that take a self-consistent treatment of element diffusion into account as well as expectations for the outer layer chemical stratification of progenitor stars upon entering the white dwarf regime. We find that PG1159 stars cannot be related to any DQ white dwarfs with low C abundances. Instead, we suggest that the latter could constitute the progeny of the giant, helium-rich RCrB stars.
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