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

TL;DR

This study investigates how primordial atmosphere loss affects the distribution of radioactive heat-producing isotopes like potassium in Earth-like exoplanets, influencing their thermal evolution and habitability.

Contribution

It introduces a model combining outgassing, impact growth, and atmospheric escape to assess how primordial atmospheres modify internal heat budgets of terrestrial exoplanets.

Findings

H₂-dominated atmospheres prevent K condensate formation at high temperatures.

Limited diffusion and escape of $^{40}$K affect the planet's internal heat budget.

Atmospheric loss impacts the thermal and tectonic evolution of exoplanets.

Abstract

The initial abundance of radioactive heat producing isotopes in the interior of a terrestrial planet 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 H$_2$-dominated primordial atmospheres of protoplanets with assumed masses between 0.55-1.0$ M_{\rm Earth}$ at the time when the gas disk evaporated. We estimate this outgassing and let these planets grow through impacts of depleted and non-depleted material that resembles the same $^{40}$K abundance of average carbonaceous chondrites until the growing protoplanets reach 1.0 $M_{\rm Earth}$. We examine different atmospheric compositions and, as a function of pressure and temperature, calculate the proportion of K by Gibbs Free Energy minimisation using the GGChem code. We find that for H$_2$-envelopes and for magma ocean surface temperatures that are $\ge$ 2500 K, no K condensates are thermally stable, so that outgassed $^{40}$K can populate the atmosphere to a great extent. However, due to magma ocean turn-over time and the limited diffusion of $^{40}$K into the upper atmosphere, from the entire $^{40}$K in the magma ocean only a fraction may be available for escaping into space. The escape rates of the primordial atmospheres and the dragged $^{40}$K are further simulated for different stellar EUV-activities with a multispecies hydrodynamic upper atmosphere evolution model. Our results lead to different abundances of heat producing elements within the fully grown planets which may give rise to different thermal and tectonic histories of terrestrial planets and their habitability conditions.