Modeling the albedo of Earth-like magma ocean planets with H2O-CO2 atmospheres

During accretion, the young rocky planets are so hot that they become endowed with a magma ocean. From that moment, the mantle convective thermal flux control the cooling of the planet and an atmosphere is created by outgassing. This atmosphere will then play a key role during this cooling phase. Studying this cooling phase in details is a necessary step to explain the great diversity of the observed telluric planets and especially to assess the presence of surface liquid water. We used here a radiative-convective 1D atmospheric model (H₂O, CO₂) to study the impact of the Bond albedo on the evolution of magma ocean planets. We derived from this model the thermal emission spectrum and the spectral reflectance of these planets, from which we calculated their Bond albedos. Compared to Marcq et al. (2017), the model now includes a new module to compute the Rayleigh scattering, and state of the art CO₂ and H₂O gaseous opacities data in the visible and infrared spectral ranges. We show that the Bond albedo of these planets depends on their surface temperature and results from a competition between Rayleigh scattering from the gases and Mie scattering from the clouds. The colder the surface temperature is, the thicker the clouds are, and the higher the Bond albedo is. We also evidence that the relative abundances of CO₂ and H₂O in the atmosphere strongly impact the Bond albedo. The Bond albedo is higher for atmospheres dominated by the CO₂, better Rayleigh scatterer than H₂O. Finally, we provide the community with an empirical formula for the Bond albedo that could be useful for future studies of magma ocean planets.