|Temperature of the Earth under present|
conditions with a solar flux of 341 W/m2,
and just before the runaway greenhouse is triggered
for a mean solar flux of 375 W/m2.
From the Leconte et al. article referenced in text.
|Cover of Science in 2014|
In 2013, Sid Perkins wrote a piece in Nature (December 11, 2013) discussing the habitable zone and summarizing the work of Jeremy Leconte at the Pierre Simon Laplace Institute in Paris (Leconte et al., Nature, 504, 268, 2013). Leconte ran the first fully three dimensional model of hot, very moist planetary atmospheres (and thus the work only applies to planets that have abundant water like the Earth; there is no evidence yet whether the newly discovered planet in Cygnus has water). Previous models had been one-dimensional and considered only how the atmospheric conditions changed in the vertical direction, ignoring horizontal transport effects, whereas this model can take account of the Hadley circulation. Leconte et al. conclude that the runaway greenhouse will take effect at a mean solar insolation of about 375 W/m2. In this model, warming of the planet causes the formation of cirrus clouds at high altitudes. Such clouds trap heat, and the heating leads to more evaporation, which leads to more clouds and thus the feedback to a greenhouse effect. The model also suggests that the large-scale circulation (not possible in 1-D models) creates cloud-free areas in the mid-latitudes that allow heat to radiate back to space. The conclusion is that the inner edge of the Solar System's habitable zone is about 142 million kilometers from the sun. Earth is at 149,600,000 kilometers so we are close to the inner edge of the habitable zone. Other authors, however, have concluded that the inner boundary could be considerably closer especially for planets that have much less water to feed the greenhouse effect (Petigura, et. al., Proc. Natl. Acad. Sci. USA 110, 19723, 2013).
Wiki has a good summary of habitable zone thermodynamics here.