Without the stabilizing influence of the Moon, the Earth's obliquity could vary significantly. Extrasolar terrestrial planets with the potential to host life may therefore have large obliquities or be subject to strong obliquity variations. We revisit the habitability of oblique planets with an energy balance climate model (EBM) allowing for dynamical transitions to ice-covered snowball states as a result of ice-albedo feedback. Despite the great simplicity of our EBM, it captures reasonably well the seasonal cycle of global energetic fluxes at Earth's surface. It also performs satisfactorily against a full-physics climate model of a highly oblique Earth, in an unusual regime of circulation dominated by heat transport from the poles to the equator. Climates on oblique terrestrial planets can violate global radiative balance through much of their seasonal cycle, which limits the usefulness of simple radiative equilibrium arguments. High obliquity planets have severe climates, with large amplitude seasonal variations, but they are not necessarily more prone to global snowball transitions than low obliquity planets. We find that terrestrial planets with massive CO2 atmospheres, typically expected in the outer regions of habitable zones, can also be subject to such dynamical snowball transitions. Some of the snowball climates investigated for CO2-rich atmospheres experience partial atmospheric collapse. Since long-term CO2 atmospheric build-up acts as a climatic thermostat for habitable planets, partial CO2 collapse could limit the habitability of such planets. A terrestrial planet's habitability may thus depend sensitively on its short-term climatic stability.
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