  A quarter of DA white dwarfs are metal polluted, yet elements heavier than
helium sink down through the stellar atmosphere on timescales of days. Hence,
these white dwarfs must be currently accreting material containing heavy
elements. Here, we consider whether the scattering of comets or asteroids from
an outer planetary system, following stellar mass loss on the asymptotic giant
branch, can reproduce these observations. We use N-body simulations to
investigate the effects of stellar mass loss on a simple system consisting of a
planetesimal belt whose inner edge is truncated by a planet. Our simulations
find that, starting with a planetesimal belt population fitted to the observed
main sequence evolution, sufficient mass is scattered into the inner planetary
system to explain the inferred heavy element accretion rates. This assumes that
some fraction of the mass scattered into the inner planetary system ends up on
star-grazing orbits, is tidally disrupted and accreted onto the white dwarf.
The simulations also reproduce the observed decrease in accretion rate with
cooling age and predict accretion rates in old (>1Gyr) white dwarfs, in line
with observations. The efficiency we assumed for material scattered into the
inner planetary system to end up on star-grazing orbits is based on a
Solar-like planetary system, since the simulations show that a single planet is
not sufficient. Although the correct level of accretion is reproduced, the
simulations predict a higher fraction of accreting white dwarfs than observed.
This could indicate that evolved planetary systems are less efficient at
scattering bodies onto star-grazing orbits or that dynamical instabilities
post-stellar mass loss cause rapid planetesimal belt depletion for a
significant fraction of systems.
