Limit cycles can reduce the width 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. Recent calculations have suggested that planets in the outer regions of the habitable zone cannot maintain stable, warm climates, but rather should oscillate between long, globally glaciated states and shorter periods of climatic warmth. Such conditions, similar to 'Snowball Earth' episodes experienced on Earth, would be inimical to the development of complex land life, including intelligent life. Here, we build upon previous studies with an updated an energy balance climate model to calculate this 'limit cycle' region of the habitable zone where such cycling would occur. We argue that an abiotic Earth would have a greater CO$_2$ partial pressure than today because plants and other biota help to enhance the storage of CO$_2$ in soil. When we tune our abiotic model accordingly, we find that limit cycles can occur but that previous calculations have overestimated their importance. For G stars like the Sun, limit cycles occur only for planets with CO$_2$ outgassing rates less than that on modern Earth. For K and M star planets, limit cycles should not occur; however, M-star planets may be inhospitable to life for other reasons. Planets orbiting late G-type and early K-type stars retain the greatest potential for maintaining warm, stable conditions. Our results suggest that host star type, planetary volcanic activity, and seafloor weathering are all important factors in determining whether planets will be prone to limit cycling. 
Jacob Haqq-Misra, Ravi Kumar Kopparapu, Natasha E. Batalha, Chester E.   Harman, James F. Kasting
astro-ph.EP astro-ph.IM physics.ao-ph