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

Context. Long-lived radioactive nuclides, such as 40K, 232Th, 235U, and 238U, 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 of 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. Aims. 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. Methods. As a case study, we present a determination of Eu abundances in the photospheres of α Cen A and B with high-resolution HARPS spectra and a strict line-by-line differential analysis. To first order, the measured Eu abundances can be converted into the abundances of 232Th, 235U, and 238U with observational constraints, while the abundance of 40K is approximated independently with a Galactic chemical evolution model. Results. Our determination shows that europium is depleted with respect to iron by ~0.1 dex and to silicon by ~0.15 dex compared to solar in the two binary components. The loci of α Cen AB at the low-ends of both [Eu/Fe] and [Eu/Si] distributions of a large sample of FGK stars further suggest significantly lower potential of radiogenic heat production in any putative terrestrial-like planet (i.e. α-Cen-Earth) in this system compared to that in rocky planets (including our own Earth) that formed around the majority of these Sun-like stars. Based on our calculations of the radionuclide concentrations in the mantle and assuming the mantle mass to be the same as that of our Earth, we find that the radiogenic heat budget in an α-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, which is 23 ± 5% and 54 ± 5% lower than that in the Hadean Earth (94.9 ± 5.5 TW) and in the modern Earth (19.0 ± 1.1 TW), respectively. Conclusions. As a consequence, mantle convection in an α-Cen-Earth is expected to be overall weaker than that of 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 predict the nature of other rocky worlds that can be tested by future observations.