Outer Limits of the Habitable Zones in Terms of Climate Mode and Climate Evolution of Earth-like Planets

We investigate the climate modes and climate evolution of Earth-like planets-specifically planets that receive lower insolation than the present Earth-to discuss the outer limits of the habitable zones (HZs) associated with main-sequence stars. The HZ outer limit is discussed in terms of the insolation above which a planet maintains liquid water on its surface (e.g., warm climate). We call this a warm start limit. However, an alternative outer limit exists above which a planet characterized by a snowball climate transitions to a warm climate, which we call a cold start limit. The cold start limit is determined by two different mechanisms: condensation of CO2 and maximum CO2 greenhouse effect. The threshold insolation is always higher than the warm start limit. We find that for the initial few billion years following the formation of a planetary system, the location of its outer HZ limit does not evolve away from the initial warm start limit. It subsequently moves in accordance with the evolution of the cold start limit. We also find that when the luminosity increase of the central star is slow relative to the decrease in the CO2 degassing rate, the location of the outer limit of the HZ may even move inward. We conclude that the cold start limit should be treated as the outer limit of the HZ given the prevailing uncertainties, including the evolution of the CO2 degassing rate and continental growth.