Figure 14 Summary of recent 1D and 3D model estimates of the location of the

Figure 14 summary of recent 1d and 3d model estimates

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Figure 14. Summary of recent 1D and 3D model estimates of the location of the inner edge for mid-K- to M-stars. The Leconte et al. [ 25 ] curve is the nominal inner edge estimate for rapidly-rotating planets, superseding the previous estimate [ 26 ]. The remaining limits are various 3D estimates for synchronously-rotating worlds. 12.2. The Effects of CO 2 and CO 2 Clouds on the Outer Edge One-dimensional modeling results suggest that 3 TRAPPIST-1 planets (e, f, and g) should be inside the classical HZ [ 208 ], which also agrees with 3D modeling simulations [ 161 ]. Another 3D study had initially argued that a dense CO 2 atmosphere cannot warm TRAPPIST-1 f and g [ 245 ], but their revised calculations now show better agreement with the other 1D and 3D results [ 246 ]. The 1D and 3D results are consistent with one another because of the high opacities that characterize atmospheres near the outer edge. Enhanced heat and dynamical transport in dense CO 2 atmospheres greatly reduce the day- to night-side temperature contrast (e.g., [ 161 , 176 , 247 ]), and so the single-column approximation made in 1D models is reasonable. However, 1D and 3D models of tidally-locked M-star planets with thinner atmospheres exhibit greater disagreement owing to the reduced day- to night-side heat transport. Nevertheless, recent work has shown how 1D models using the weak thermal gradient approximation can produce results for tidally-locked planets that are not only consistent with those of 3D models, but are able to generate almost identical thermal phase curves for observational purposes (e.g., [ 248 , 249 ]). Moreover, given that the 1D models that have been used to compute HZ boundaries are unable to self-consistently compute relative humidity (e.g., [ 1 , 26 , 51 ]), such calculations typically assume a surface value of 100%, which is wetter than real atmospheres. Despite this simplification, the 1D assumption does not significantly overestimate the outer edge distance because water vapor concentrations at the outer edge are low and water vapor absorption is minimal [ 216 , 250 ]. Large decreases (>10%) in the outer edge distance are predicted only at extremely low (~0%), and likely unrealistic, values of relative humidity [ 216 ]. In addition, CO 2 clouds should form in these atmospheres (e.g., [ 38 ]), producing significant greenhouse warming (several 10 s of K) if cloud coverage approaches ~100% [ 38 , 39 ]. However, the warming from this mechanism is greatly reduced at lower cloud fractions. Recent 3D simulations of early Mars predict that a typical CO 2 cloud coverage may be ~50%, which reduces the surface warming
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Geosciences 2018 , 8 , 280 29 of 48 from CO 2 clouds to 15 K, even assuming idealized parameters that maximize this warming [ 39 ]. Plus, all previous studies had only used two streams in their radiative transfer calculations. After improving accuracy by increasing the number of streams, CO 2 clouds were found to provide almost no net greenhouse effect [ 40 ]. This is another reason why the 1D and 3D outer edge results appear to be consistent with one another.
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