  In the outer regions of the habitable zone, the risk of transitioning into a
globally frozen "snowball" state poses a threat to the habitability of planets
with the capacity to host water-based life. We use a one-dimensional energy
balance climate model (EBM) to examine how obliquity, spin rate, orbital
eccentricity, and ocean coverage might influence the onset of such a snowball
state. For an exoplanet, these parameters may be strikingly different from the
values observed for Earth. Since, for constant semimajor axis, the annual mean
stellar irradiation scales with (1-e^2)^(-1/2), one might expect the greatest
habitable semimajor axis (for fixed atmospheric composition) to scale as
(1-e^2)^(-1/4). We find that this standard ansatz provides a reasonable lower
bound on the outer boundary of the habitable zone, but the influence of
obliquity and ocean fraction can be profound in the context of planets on
eccentric orbits. For planets with eccentricity 0.5, our EBM suggests that the
greatest habitable semimajor axis can vary by more than 0.8 AU (78%!) depending
on obliquity, with higher obliquity worlds generally more stable against
snowball transitions. One might also expect that the long winter at an
eccentric planet's apoastron would render it more susceptible to global
freezing. Our models suggest that this is not a significant risk for Earth-like
planets around Sun-like stars since such planets are buffered by the thermal
inertia provided by oceans covering at least 10% of their surface. Since
planets on eccentric orbits spend much of their year particularly far from the
star, such worlds might turn out to be especially good targets for direct
observations with missions such as TPF-Darwin. Nevertheless, the extreme
temperature variations achieved on highly eccentric exo-Earths raise questions
about the adaptability of life to marginally or transiently habitable
conditions.
