  Polluted white dwarfs serve as astrophysical mass spectrometers - their
photospheric abundances are used to infer the composition of planetary objects
that accrete onto them. We show that due to asymmetries in the accretion
process, the composition of the material falling onto a star may vary with time
during the accretion of a single planetary body. Consequently, the
instantaneous photospheric abundances of white dwarfs do not necessarily
reflect the bulk composition of their pollutants, especially when their
diffusion timescales are short. In particular, we predict that when an asteroid
with an iron core tidally disrupts around a white dwarf, a larger share of its
mantle is ejected, and that the core/mantle fraction of the accreting material
varies with time during the event. Crucially, this implies that the core
fraction of differentiated pollutants cannot be determined for white dwarfs
with short diffusion timescales, which sample only brief episodes of longer
accretion processes. The observed population of polluted white dwarfs backs up
the proposed theory. More white dwarfs have accreted material with high Fe/Ca
than low Fe/Ca relative to stellar abundance ratios, indicating the ejection of
mantle material. Additionally, we find tentative evidence that the accretion
rate of iron decreases more rapidly than that of magnesium or calcium, hinting
at variability of the accreted composition. Further corroboration of the
proposed theory will come from the up-coming analysis of large samples of young
white dwarfs.
