Europium as a lodestar: diagnosis of radiogenic heat production in terrestrial exoplanets

Abstract

Long-lived radioactive nuclides, such as ${}^{40}$K, ${}^{232}$Th, ${}^{235}$U and ${}^{238}$U, contribute to persistent heat production in the mantle of terrestrial-type planets. As refractory elements, the concentrations of Th and U in a terrestrial exoplanet are implicitly reflected in the photospheric abundances in the stellar host. However, a robust determination of these stellar abundances is difficult in practice owing to the general paucity and weakness of the relevant spectral features. We draw attention to the refractory, $r-$process element europium, which may be used as a convenient and practical proxy for the population analysis of radiogenic heating in exoplanetary systems. As a case study, we present a determination of Eu abundances in the photospheres of $\alpha$ Cen A and B. We find that europium is depleted with respect to iron by $\sim$ 0.1 dex and to silicon by $\sim$ 0.15 dex compared to solar in both binary components. To first order, the measured Eu abundances can be converted to the abundances of ${}^{232}$Th, ${}^{235}$U and ${}^{238}$U with observational constraints while the abundance of ${}^{40}$K is approximated independently with a Galactic chemical evolution model. We find that the radiogenic heat budget in an $\alpha$-Cen-Earth is $73.4_{-6.9}^{+8.3}$ TW upon its formation and $8.8_{-1.3}^{+1.7}$ TW at the present day, respectively $23\pm 5$ % and $54\pm 5$ % lower than that in the Hadean and modern Earth. As a consequence, mantle convection in an $\alpha$-Cen-Earth is expected to be overall weaker than that of the Earth (assuming other conditions are the same) and thus such a planet would be less geologically active, suppressing its long-term potential to recycle its crust and volatiles. With Eu abundances being available for a large sample of Sun-like stars, the proposed approach can extend our ability to make predictions about the nature of other rocky worlds.

Accepted for publication in Astronomy & Astrophysics. 11 pages, 4 figures, and 4 tables

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