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The accretion of planetesimals onto white dwarf atmospheres allowsdetermination of the composition of this polluting material. This compositionis usually inferred from observed pollution levels by assuming it originatedfrom a single body. This paper instead uses a stochastic model whereinpolluting planetesimals are chosen randomly from a mass distribution, findingthat the single body assumption is invalid in >20% of cases. Planetesimalcompositions are modelled assuming parent bodies that differentiated into core,mantle and crust components. Atmospheric levels of Ca, Mg and Fe in the modelare compared to a sample of 230 DZ white dwarfs for which such pollution ismeasured. A good fit is obtained when each planetesimal has its core, mantleand crust fractions chosen independently from logit-normal distributions whichlead to average mass fractions of $f_\text{Cru}=0.15$, $f_\text{Man}=0.49$ and$f_\text{Cor}=0.36$. However, achieving this fit requires a factor 4 depletionof Mg relative to stellar material. This depletion is unlikely to originate inplanetesimal formation processes, but might occur from heating while the staris on the giant branch. Alternatively the accreted material has stellarabundance, and either the inferred low Mg abundance was caused by an incorrectassumption that Mg sinks slower than Ca and Fe, or there are unmodelled biasesin the observed sample. Finally, the model makes predictions for the timescaleon which the observed pollutant composition varies, which should be the longerof the sinking and disc timescales, implying variability on decadal timescalesfor DA white dwarfs.

Modelling the distributions of white dwarf atmospheric pollution: a low Mg abundance for accreted planetesimals?