  In the search for life on Earth-like planets around other stars, the first
(and likely only) information will come from the spectroscopic characterization
of the planet's atmosphere. Of the countless number of chemical species
terrestrial life produces, only a few have the distinct spectral features and
the necessary atmospheric abundance to be detectable. The easiest of these
species to observe in Earth's atmosphere is O$_{2}$ (and its photochemical
byproduct, O$_{3}$). But O$_{2}$ can also be produced abiotically by photolysis
of CO$_{2}$, followed by recombination of O atoms with each other. CO is
produced in stoichiometric proportions. Whether O$_{2}$ and CO can accumulate
to appreciable concentrations depends on the ratio of far-UV to near-UV
radiation coming from the planet's parent star and on what happens to these
gases when they dissolve in a planet's oceans. Using a one-dimensional
photochemical model, we demonstrate that O$_{2}$ derived from CO$_{2}$
photolysis should not accumulate to measurable concentrations on planets around
F- and G-type stars. K-star, and especially M-star planets, however, may build
up O$_{2}$ because of the low near-UV flux from their parent stars, in
agreement with some previous studies. On such planets, a 'false positive' for
life is possible if recombination of dissolved CO and O$_{2}$ in the oceans is
slow and if other O$_{2}$ sinks (e.g., reduced volcanic gases or dissolved
ferrous iron) are small. O$_{3}$, on the other hand, could be detectable at UV
wavelengths ($\lambda$ < 300 nm) for a much broader range of boundary
conditions and stellar types.
