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Over 1500 DBZ or DZ white dwarfs (WDs) have been observed so far, andpolluted atmospheres with metal elements have been found among these WDs. Thesurface heavy element abundances of known DBZ or DZ WDs show an evolutionarysequence. By using Modules for Experiments in Stellar Evolution, we create DBWDs, and simulate the element diffusion due to high gravitational fields andthe metal-rich material accretion coming from the planet disrupted by the WD.In our models, the input parameters ($\alpha_{\rm MLT}$, $\alpha_{\rm th}$ and$Z$) have very weak effect on DB WD structures including interior temperatures,chemical profiles and convective zones.The mass-accretion rate and theeffective temperature of DB WDs determine the abundances of heavy elements. Theevolutionary sequence of Ca element for about 1500 observed DB or DBZ WDscannot be explained by the model with a constant mass-accretion rate, but isconsistent well with the model in which the mass-accretion rate decreases byone power law when $T_{\rm eff}>10$ kK and slightly increases by another powerlaw when $T_{\rm eff}<10$ kK. The observed DB WD evolutionary sequence of heavyelement abundances originates from WD cooling and the change of mass-accretionrate.

Formation, diffusion and accreting pollution of DB white dwarfs