The presence of valleys on ancient terrains of Mars suggest that liquid water flowed on the martian surface 3.8 billion years ago or before. The above-freezing temperatures required to explain valley formation could have been transient, in response t
o frequent large meteorite impacts on early Mars, or they could have been caused by long-lived greenhouse warming. Climate models that consider only the greenhouse gases carbon dioxide and water vapor have been unable to recreate warm surface conditions, given the lower solar luminosity at that time. Here we use a one-dimensional climate model to demonstrate that an atmosphere containing 1.3-4 bar of CO2 and water vapor, along with 5 to 20 percent H2, could have raised the mean surface temperature of early Mars above the freezing point of water. Vigorous volcanic outgassing from a highly reduced early martian mantle is expected to provide sufficient atmospheric H2 and CO2, the latter from the photochemical oxidation of outgassed CH4 and CO, to form a CO2-H2 greenhouse. Such a dense early martian atmosphere is consistent with independent estimates of surface pressure based on cratering data.
The habitable zone (HZ) around a star is typically defined as the region where a rocky planet can maintain liquid water on its surface. That definition is appropriate, because this allows for the possibility that carbon-based, photosynthetic life exi
sts on the planet in sufficient abundance to modify the planets atmosphere in a way that might be remotely detected. Exactly what conditions are needed, however, to maintain liquid water remains a topic for debate. Historically, modelers have restricted themselves to water-rich planets with CO2 and H2O as the only important greenhouse gases. More recently, some researchers have suggested broadening the definition to include arid, Dune planets on the inner edge and planets with captured H2 atmospheres on the outer edge, thereby greatly increasing the HZ width. Such planets could exist, but we demonstrate that an inner edge limit of 0.59 AU or less is physically unrealistic. We further argue that conservative HZ definitions should be used for designing future space-based telescopes, but that optimistic definitions may be useful in interpreting the data from such missions. In terms of effective solar flux, Seff, the recently recalculated HZ boundaries are: recent Venus-1.78, runaway greenhouse-1.04, moist greenhouse-1.01, maximum greenhouse-0.35, early Mars-0.32. Based on a combination of different HZ definitions, the frequency of potentially Earth-like planets around late-K and M stars observed by Kepler is in the range of 0.4-0.5.
