Linking the Evolution of Terrestrial Interiors and an Early Outgassed Atmosphere to Astrophysical Observations

Current and future exoplanet observations will favour the detection and characterisation of hot and warm Earth-like planets, potentially with large outgassed atmospheres. We combine a coupled interior-atmosphere model with static structure calculations to track the evolving radius of a hot rocky planet that is outgassing CO2 and H2 O. Synthetic emission and transmission spectra are generated for CO2 and H2 O dominated atmospheres. Our results demonstrate that a hot molten planet can have a radius several percent larger (about 5%, assuming Earth-like core size) than its equivalent solid counterpart. Hence a molten or partially molten mantle may explain the larger radii of some close-in exoplanets that are subjected to intense insolation and/or tidal heating. Outgassing of a low molar mass species (such as H2 O, compared to CO2 ) can combat the continual contraction of a planetary mantle and even marginally increase the planetary radius. Atmospheres dominated by CO2 suppress the outgassing of H2 O to a greater extent than previously realised, since previous studies have applied an erroneous relationship between volatile mass and partial pressure. Furthermore, the formation of a lid at the surface of a cooling magma ocean may tie the outgassing of H2 O to the efficiency of heat transport through the lid, rather than the radiative timescale of the atmosphere. We further use our models to generate synthetic transmission and emission data to aid the detection and characterisation of rocky planets via transits and secondary eclipses. Atmospheres of terrestrial planets around M-stars that are dominated by CO2 versus H2O could be distinguished by future observing facilities that have extended wavelength coverage (e.g., JWST). Incomplete magma ocean crystallisation, as may be the case for close-in terrestrial planets, or full or part retention of an early outgassed atmosphere, should be considered in the interpretation of observational data from current and future observing facilities.