As lower-mass stars often host multiple rocky planets, gravitational interactions among planets can have significant effects on climate and habitability over long timescales. Here we explore a specific case, Kepler-62f (Borucki et al., 2013), a potentially habitable planet in a five-planet system with a K2V host star. N-body integrations reveal the stable range of initial eccentricities for Kepler-62f is 0.00 £ e £ 0.32, absent the effect of additional, undetected planets. We simulate the tidal evolution of Kepler-62f in this range and find that, for certain assumptions, the planet can be locked in a synchronous rotation state. Simulations using the 3-D Laboratoire de Me´te´orologie Dynamique (LMD) Generic global climate model (GCM) indicate that the surface habitability of this planet is sensitive to orbital configuration. With 3 bar of CO2 in its atmosphere, we find that Kepler-62f would only be warm enough for surface liquid water at the upper limit of this eccentricity range, providing it has a high planetary obliquity (between 60 and 90). A climate similar to that of modern-day Earth is possible for the entire range of stable eccentricities if atmospheric CO2 is increased to 5 bar levels. In a low-CO2 case (Earth-like levels), simulations with version 4 of the Community Climate System Model (CCSM4) GCM and LMD Generic GCM indicate that increases in planetary obliquity and orbital eccentricity coupled with an orbital configuration that places the summer solstice at or near pericenter permit regions of the planet with above-freezing surface temperatures. This may melt ice sheets formed during colder seasons. If Kepler-62f is synchronously rotating and has an ocean, CO2 levels above 3 bar would be required to distribute enough heat to the nightside of the planet to avoid atmospheric freeze-out and permit a large enough region of open water at the planet’s substellar point to remain stable. Overall, we find multiple plausible combinations of orbital and atmospheric properties that permit surface liquid water on Kepler-62f.

Planetary climate can be affected by the interaction of the host star spectral energy distribution with the wavelength-dependent reflectivity of ice and snow. In this study, we explored this effect with a one-dimensional (1-D), line-by-line, radiative transfer model to calculate broadband planetary albedos as input to a seasonally varying, 1-D energy balance climate model. A three-dimensional (3-D) general circulation model was also used to explore the atmosphere’s response to changes in incoming stellar radiation, or instellation, and surface albedo. Using this hierarchy of models, we simulated planets covered by ocean, land, and water-ice of varying grain size, with incident radiation from stars of different spectral types. Terrestrial planets orbiting stars with higher near-UV radiation exhibited a stronger ice-albedo feedback. We found that ice extent was much greater on a planet orbiting an F-dwarf star than on a planet orbiting a G-dwarf star at an equivalent flux distance, and that ice-covered conditions occurred on an F-dwarf planet with only a 2% reduction in instellation relative to the present instellation on Earth, assuming fixed CO2 (present atmospheric level on Earth). A similar planet orbiting the Sun at an equivalent flux distance required an 8% reduction in instellation, while a planet orbiting an Mdwarf star required an additional 19% reduction in instellation to become ice-covered, equivalent to 73% of the modern solar constant. The reduction in instellation must be larger for planets orbiting cooler stars due in large part to the stronger absorption of longer-wavelength radiation by icy surfaces on these planets in addition to stronger absorption by water vapor and CO2 in their atmospheres, which provides increased downwelling longwave radiation. Lowering the IR and visible-band surface ice and snow albedos for an M-dwarf planet increased the planet’s climate stability against changes in instellation and slowed the descent into global ice coverage. The surface ice-albedo feedback effect becomes less important at the outer edge of the habitable zone, where atmospheric CO2 could be expected to be high such that it maintains clement conditions for surface liquid water. We showed that *3–10 bar of CO2 will entirely mask the climatic effect of ice and snow, leaving the outer limits of the habitable zone unaffected by the spectral dependence of water ice and snow albedo. However, less CO2 is needed to maintain open water for a planet orbiting an M-dwarf star than would be the case for hotter main-sequence stars