The Maximal Runaway Temperature of Earth-like Planets

TL;DR

This paper generalizes the semi-gray model to determine the maximum possible temperature of Earth-like planets, showing that greenhouse effects saturate and depend on star distance, atmospheric properties, and wavelength-dependent optical thickness.

Contribution

It introduces a generalized model for planetary greenhouse effects, establishing a universal maximum temperature limit independent of greenhouse gas nature.

Findings

Maximum temperature for Earth-like planets is around 1200-1300K.

Saturation occurs via short-wavelength or FIR radiation depending on atmospheric optical properties.

Planetary radiation shifts towards NIR when short-wavelength saturation dominates.

Abstract

We generalize the problem of the semi-gray model to cases in which a non-negligible fraction of the stellar radiation falls on the long-wavelength range, and/or that the planetary long-wavelength emission penetrates into the transparent short wavelength domain of the absorption. Second, applying the most general assumptions and independently of any particular properties of an absorber, we show that the greenhouse effect saturates and any Earth-like planet has a maximal temperature which depends on the type of and distance to its main-sequence star, its albedo and the primary atmospheric components which determine the cutoff frequency below which the atmosphere is optically thick. For example, a hypothetical convection-less planet similar to Venus, that is optically thin in the visible, could have at most a surface temperature of 1200-1300K irrespective of the nature of the greenhouse gas. We show that two primary mechanisms are responsible for the saturation of the runaway greenhouse effect, depending on the value of the wavelength above which the atmosphere becomes optically thick. Unless this wavelength is small and resides in the optical region, saturation is achieved by radiating the thermal flux of the planet through the short wavelength tail of the thermal distribution. This has the observational implication, the radiation from such a planet should be skewed towards the NIR. Otherwise, saturation takes place by radiating through windows in the FIR.