Modification of the radioactive heat budget of Earth-like exoplanets by the loss of primordial atmospheres

The initial abundance of radioactive heat producing isotopes in the interior of terrestrial planets are important drivers of its thermal evolution and the related tectonics and possible evolution to an Earth-like habitat. The moderately volatile element K can be outgassed from a magma ocean into H₂-dominated primordial atmospheres of protoplanets with assumed masses between 0.55 and 1.0M_Earth at the time when the gas disc evaporated. We estimate this outgassing and let these planets grow through impacts of depleted and non-depleted material that resembles the same ⁴⁰K abundance of average carbonaceous chondrites until the growing protoplanets reach 1.0M_Earth. We examine different atmospheric compositions and, as a function of pressure and temperature, calculate the proportion of K by Gibbs Free Energy minimization using the GGCHEM code. We find that for H₂-envelopes and for magma ocean surface temperatures that are ≥ 2500 K, no K condensates are thermally stable, so that outgassed ⁴⁰K can populate the atmosphere to a great extent. However, due to magma ocean turnover time and the limited diffusion of ⁴⁰K into the upper atmosphere, from the entire ⁴⁰K in the magma ocean only a fraction may be available for escaping into space. The escape rates of the primordial atmospheres and the dragged ⁴⁰K are simulated for different stellar EUV activities with a multispecies hydrodynamic upper atmosphere evolution model. Our results show that one can expect that different initial abundances of heat producing elements will result in different thermal and tectonic histories of terrestrial planets and their habitability conditions.