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This paper explores how the stochastic accretion of planetesimals onto whitedwarfs would be manifested in observations of their atmospheric pollution.Archival observations of pollution levels for unbiased samples of DA and non-DAwhite dwarfs are used to derive the distribution of accretion rates, confirmingthat rates become systematically lower as sinking time is decreased, with nodiscernable dependence on cooling age. The accretion rates expected fromplanetesimals that are all the same mass (ie, a mono-mass distribution) areexplored both analytically and using a Monte Carlo model, quantifying howmeasured accretion rates inevitably depend on sinking time, since differentsinking times probe different times since the last accretion event. However,that dependence is so dramatic that a mono-mass distribution can be excluded.Consideration of accretion from a broad distribution of planetesimal massesuncovers an important conceptual difference: accretion is continuous (ratherthan stochastic) for planetesimals below a certain mass, and the accretion ofsuch planetesimals determines the rate typically inferred from observations;smaller planetesimals dominate the rates for shorter sinking times. Areasonable fit to the observationally inferred accretion rate distributions isfound with model parameters consistent with a collisionally evolved massdistribution up to Pluto-mass, and an underlying accretion rate distributionconsistent with that expected from descendants of debris discs of main sequenceA stars. With these parameters, while both DA and non-DA white dwarfs accretefrom the same broad planetesimal distribution, this model predicts that thepollution seen in DAs is dominated by the continuous accretion of <35kmobjects, and that in non-DAs by >35km objects (though the dominant size variesbetween stars by around an order of magnitude from this value)...

Stochastic accretion of planetesimals onto white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution