  In planetary nebulae, abundances of oxygen and other heavy elements derived
from optical recombination lines are systematically higher than those derived
from collisionally excited lines. We investigate the hypothesis that the
destruction of solid bodies may produce pockets of cool, high-metallicity gas
that could explain these abundance discrepancies. Under the assumption of
maximally efficient radiative ablation, we derive two fundamental constraints
that the solid bodies must satisfy in order that their evaporation during the
planetary nebula phase should generate a high enough gas phase metallicity. A
local constraint implies that the bodies must be larger than tens of meters,
while a global constraint implies that the total mass of the solid body
reservoir must exceed a few hundredths of a solar mass. This mass greatly
exceeds the mass of any population of comets or large debris particles expected
to be found orbiting evolved low- to intermediate-mass stars. We therefore
conclude that contemporaneous solid body destruction cannot explain the
observed abundance discrepancies in planetary nebulae. However, similar
arguments applied to the sublimation of solid bodies during the preceding
asymptotic giant branch (AGB) phase do not lead to such a clear-cut conclusion.
In this case, the required reservoir of volatile solids is only one
ten-thousandth of a solar mass, which is comparable to the most massive debris
disks observed around solar-type stars, implying that this mechanism may
contribute to abundance discrepancies in at least some planetary nebulae, so
long as mixing of the high metallicity gas is inefficient.
