Insolation patterns on eccentric exoplanets
Several studies have found that synchronously-rotating Earth-like planets in the habitable zones of M-dwarf stars should exhibit an “eyeball” climate pattern, with a pupil of open ocean facing the parent star, and ice everywhere else. Recent work on eccentric exoplanets by Wang et al. (Wang, Y., Tian, F., Hu, Y. [2014b] Astrophys. J. 791, L12) has extended this conclusion to the 2:1 spin–orbit resonance as well, where the planet rotates twice during one orbital period. However, Wang et al. also found that the 3:2 and 5:2 half-odd resonances produce a zonally-striped climate pattern with polar icecaps instead. Unfortunately, they used incorrect insolation functions for the 3:2 and 5:2 resonances whose long-term time averages are essentially independent of longitude.
This paper presents the correct insolation patterns for eccentric exoplanets with negligible obliquities in the 0:1, 1:2, 1:1, 3:2, 2:1, 5:2, 3:1, 7:2, and 4:1 spin–orbit resonances. I confirm that the mean insolation is distributed in an eyeball pattern for integer resonances; but for half-odd resonances, the mean insolation takes a “double-eyeball” pattern, identical over the “eastern” and “western” hemispheres. Presuming that liquids, ices, clouds, albedo, and thermal emission are similarly distributed, this has significant implications for the observation and interpretation of potentially habitable exoplanets.
Finally, whether a striped ball, eyeball, or double-eyeball pattern emerges, the possibility exists that long-term build-up of ice (or liquid) away from the hot spots may alter the planet’s inertia tensor and quadrupole moments enough to re-orient the planet, ultimately changing the distribution of liquid and ice.