  Understanding when global glaciations occur on Earth-like planets is a major
challenge in climate evolution research. Most models of how greenhouse gases
like CO2 evolve with time on terrestrial planets are deterministic, but the
complex, nonlinear nature of Earth's climate history motivates study of
non-deterministic climate models. Here a maximally simple stochastic model of
CO2 evolution and climate on an Earth-like planet with an imperfect CO2
thermostat is investigated. It is shown that as stellar luminosity is increased
in this model, the decrease in the average atmospheric CO concentration renders
the climate increasingly unstable, with excursions to a low-temperature state
common once the received stellar flux approaches that of present-day Earth.
Unless climate feedbacks always force the variance in CO2 concentration to
decline rapidly with received stellar flux, this means that terrestrial planets
near the inner edge of the habitable zone may enter Snowball states quite
frequently. Observations of the albedos and color variation of terrestrial-type
exoplanets should allow this prediction to be tested directly in the future.
