Evolutionary calculations of carbon dredge-up in helium envelope white dwarfs

We investigate the evolution of cooling helium atmosphere white dwarfs using a full evolutionary code, specifically developed for following the effects of element diffusion and gravitational settling on white dwarf cooling. The major difference between this work and previous work is that we use more recent opacity data from the OPAL project. Since, in general, these opacities are higher than those available ten years ago, at a given effective temperature, convection zones go deeper than in models with older opacity data. Thus convective dredge-up of observationally detectable carbon in helium atmosphere white dwarfs can occur for thicker helium layers than found by Pelletier et al (1986). We find that the range of observed C to He ratios in different DQ white dwarfs of similar effective temperature is well explained by a range of initial helium layer mass between $10^{-3}$ and $10^{-2} M_{\odot}$, in good agreement with stellar evolution theory, assuming a typical white dwarf mass of $0.6 M_{\odot}$. We also predict that oxygen will be present in DQ white dwarf atmospheres in detectable amounts if the helium layer mass is near the lower limit compatible with stellar evolution theory. Determination of the oxygen abundance has the potential of providing information on the profile of oxygen in the core and hence on the important $^{12}$C$(\alpha,\gamma)^{16}$O reaction rate.