Thermal radiation of magma ocean planets using a 1‐D radiative‐convective model of H2O‐CO2 atmospheres

This paper presents an updated version of the simple 1‐D radiative‐convective H2O‐CO2 atmospheric model from Marcq (2012) and used by Lebrun et al. (2013) in their coupled interior‐atmosphere model. This updated version includes a correction of a major miscalculation of the outgoing longwave radiation (OLR) and extends the validity of the model (P coordinate system, possible inclusion of N2, and improved numerical stability). It confirms the qualitative findings of Marcq (2012), namely, (1) the existence of a blanketing effect in any H2O‐dominated atmosphere: the outgoing longwave radiation (OLR) reaches an asymptotic value, also known as Nakajima's limit and first evidenced by Nakajima et al. (1992), around 280 W/m2 neglecting clouds, significantly higher than our former estimate from Marcq (2012). (2) The blanketing effect breaks down for a given threshold temperature Tϵ, with a fast increase of OLR with increasing surface temperature beyond this threshold, making extrasolar planets in such an early stage of their evolution easily detectable near 4 μm provided they orbit a red dwarf. Tϵ increases strongly with H2O surface pressure, but increasing CO2 pressure leads to a slight decrease of Tϵ. (3) Clouds act both by lowering Nakajima's limit by up to 40% and by extending the blanketing effect, raising the threshold temperature Tϵ by about 10%. Plain Language Summary Recently formed Earth‐sized planets experience a “magma ocean” stage, where molten rocks extend from the core up to the surface. These planets are able to cool themselves by radiating more heat through their thick atmospheres than they absorb from their parent star. We have investigated the effect of the total atmospheric content (assumed to consist mostly of water vapor and carbon dioxide) and of the surface temperature of the magma ocean upon the rapidity of the cooling. Our main finding is that there are two stages: for very high surface temperatures, cooling is fast, and only thin clouds can form. Such planets would be quite easily detected since they radiate very efficiently in the infrared range. Conversely, relatively cool surface temperatures lead to cooler upper atmospheres, harboring thick water clouds. Such planets would be very difficult to distinguish from more mature planets such as Earth or Venus from the point of view of a remote observer. Key Points Thermal blanketing confirmed at almost equal to 280 W/m2, for steam‐dominated atmospheres (Nakajima's limit) around magma ocean p