Limit cycles at the outer edge of the habitable zone

The liquid water habitable zone (HZ) describes the orbital distance at which a terrestrial planet can maintain above-freezing conditions through regulation by the carbonate-silicate cycle. Calculations with one-dimensional climate models predict that the inner edge of the HZ is limited by water loss through a runaway greenhouse, while the outer edge of the HZ is bounded by the maximum greenhouse effect of carbon dioxide. This classic picture of the HZ continues to guide interpretation of exoplanet discoveries; however, recent calculations have shown that terrestrial planets near the outer edge of the HZ may exhibit other behaviors that affect their habitability. Here I discuss results from a hierarchy of climate models to understand the stellar environments most likely to support a habitable planet. I present energy balance climate model calculations showing the conditions under which planets in the outer regions of the habitable zone should oscillate between long, globally glaciated states and shorter periods of climatic warmth, known as `limit cycles.' Such conditions would be inimical to the development of complex land life, including intelligent life. Limit cycles may also provide an explanation for fluvial features on early Mars, although this requires additional greenhouse warming by hydrogen. These calculations show that the net volcanic outgassing rate and the propensity for plant life to sequester carbon dioxide are critical factors that determine the susceptibility of a planet to limit cycling. I argue that planets orbiting mid G- to mid K-type stars offer more opportunity for supporting advanced life than do planets around F-type stars or M-type stars.