  Although discs of dust and gas have been observed orbiting white dwarfs, the
origin of this circumstellar matter is uncertain. We hypothesize that the
in-situ breakup of small bodies such as asteroids spun to fission during the
giant branch phases of stellar evolution provides an important contribution to
this debris. The YORP effect, which arises from radiation pressure, accelerates
the spin rate of asymmetric asteroids, which can eventually shear themselves
apart. This pressure is maintained and enhanced around dying stars because the
outward push of an asteroid due to stellar mass loss is insignificant compared
to the resulting stellar luminosity increase. Consequently, giant star
radiation will destroy nearly all bodies with radii in the range 100 m - 10 km
that survive their parent star's main sequence lifetime within a distance of
about 7 au; smaller bodies are spun apart to their strongest, competent
components. This estimate is conservative, and would increase for highly
asymmetric shapes or incorporation of the inward drag due to giant star stellar
wind. The resulting debris field, which could extend to thousands of au, may be
perturbed by remnant planetary systems to reproduce the observed dusty and
gaseous discs which accompany polluted white dwarfs.
