Ice Caps and Ice Belts: The Effects of Obliquity on Albedo Feedback

For obliquity angles exceeding 55º, the annual mean insolation is largest at the poles and weakest at the equator. If such a planet were to have stable partial snow and ice cover, it would likely be in the form of a belt about the equator rather than polar caps. Motivated by the large diversity of exoplanets, we use an analytical model of planetary climate to investigate the stability of ice caps and ice belts over a wide range of parameters. The model is a non-dimensional form of the well-known diffusive Energy Balance Model (EBM), representing the interplay between insolation, heat transport and albedo feedback on a spherical planet. We present a complete analytical solution to the annual-mean model valid for any obliquity. We partially validate our analytical results against numerical solutions of a seasonal model. We find that multiple equilibria and unstable transitions between climate states (ice-free, Snowball, or ice cap/belt) occur over wide swaths of parameter space at both high and low obliquity. We discuss the physics of "Large Ice Belt Instability" and "Small Ice Belt Instability" at high obliquity compared to their more familiar low-obliquity analogs. Our findings suggest that stable ice belts are relatively rare. We estimate that about 3/4 to 4/5 of all planets with stable partial ice cover would be in the form of Earth-like polar caps. High-obliquity planets are more likely to remain ice-free to the outer edge of their habitable zone.