Formation, diffusion, and accreting pollution of DB white dwarfs

Context. Over 1500 DBZ or DZ white dwarfs (WDs) have been observed so far, and polluted atmospheres with metal elements have been found among these WDs. The surface heavy element abundances of known DBZ or DZ WDs show an evolutionary sequence. Cooling, diffusion, and accretion are important physical processes in WD evolution which can alter the element abundances of the WD surface. Aims. Using the stellar evolutionary code, we investigated the DB WD formation and the effects of input parameters −, including the mixing length parameter (αMLT), thermohaline mixing efficiency (αth), and the metallicity (Z) −, on the structures of these DB WDs. The impacts of the convective zone mass (Mcvz), cooling timescales, diffusive timescales (τdiff), and the mass-accretion rate (Ṁa) on the element abundances of the WDs’ surfaces are discussed. By comparing the theoretical model results with observations, we try to understand the evolutionary sequence of the heavy element abundance on DBZ WD surfaces. Methods. By using Modules for Experiments in Stellar Evolution, we created DB WDs, and simulated the element diffusion due to high gravitational fields and the metal-rich material accretion coming from the planet disrupted by the WD. Then, we calculated the element abundances of these DB WDs for a further comparison with observations. Results. In our models, the input parameters (αMLT, αth, and Z) have a very weak effect on DB WD structures, including interior temperatures, chemical profiles, and convective zones. They hardly affect the evolution of the heavy elements on the surface of DB WDs. The mass-accretion rate and the effective temperature of DB WDs determine the abundances of heavy elements. The evolutionary sequence of the Ca element for about 1500 observed DB or DBZ WDs cannot be explained by the model with a constant mass-accretion rate, but it is very consistent with the model in which the mass-accretion rate decreases by one power law when Teff > 10 kK and it slightly increases by another power law when Teff < 10 kK. Conclusions. The observed DB WD evolutionary sequence of heavy element abundances originates from WD cooling and the change in the mass-accretion rate