  (Abridged) We show that sizeable fractions of incident ionizing radiation
from stochastic astrophysical sources can be redistributed to biologically and
chemically important UV wavelengths, a significant fraction of which can reach
the surface. This redistribution is mediated by secondary electrons, resulting
from Compton scattering and X-ray photoabsorption, with energies low enough to
excite atmospheric molecules and atoms, resulting in a rich aurora-like
spectrum. We calculate the fraction of energy redistributed into biologically
and chemically important wavelength regions for spectra characteristic of
stellar flares and supernovae using a Monte-Carlo transport code written for
this problem and then estimate the fraction of this energy that is transmitted
from the atmospheric altitudes of redistribution to the surface for a few
illustrative cases. Redistributed fractions are found to be of order 1%, even
in the presence of an ozone shield. This result implies that planetary
organisms will be subject to mutationally significant, if intermittent,
fluences of UV-B and harder radiation even in the presence of a narrow-band UV
shield like ozone. We also calculate the surficial transmitted fraction of
ionizing radiation and redistributed ultraviolet radiation for two illustrative
evolving Mars atmospheres whose initial surface pressures were 1 bar. Our
results suggest that coding organisms on planets orbiting low-mass stars (and
on the early Earth) may evolve very differently than on contemporary Earth,
with diversity and evolutionary rate controlled by a stochastically varying
mutation rate and frequent hypermutation episodes.
