Radiogenic power and geoneutrino luminosity of the Earth and other terrestrial bodies through time

TL;DR

This paper quantifies Earth's radiogenic heat production and geoneutrino luminosity over 4.57 billion years, updating decay parameters and element abundances to improve understanding of Earth's thermal history and neutrino emissions.

Contribution

It provides a comprehensive model of Earth's radiogenic heat and neutrino luminosity evolution using updated nuclear physics and geochemical data, including a simplified equation for current heat production.

Findings

Present-day Earth's radiogenic heat: 19.9±3.0 TW

Early Earth radiogenic heating was 10^3 to 10^4 times greater

Maximum energy from short-lived radionuclide $^{26}$Al is comparable to Earth's gravitational binding energy

Abstract

We report the Earth's rate of radiogenic heat production and (anti)neutrino luminosity from geologically relevant short-lived radionuclides (SLR) and long-lived radionuclides (LLR) using decay constants from the geological community, updated nuclear physics parameters, and calculations of the $\beta$ spectra. We track the time evolution of the radiogenic power and luminosity of the Earth over the last 4.57 billion years, assuming an absolute abundance for the refractory elements in the silicate Earth and key volatile/refractory element ratios (e.g., Fe/Al, K/U, and Rb/Sr) to set the abundance levels for the moderately volatile elements. The relevant decays for the present-day heat production in the Earth ($19.9\pm3.0$ TW) are from $^{40}$K, $^{87}$Rb, $^{147}$Sm, $^{232}$Th, $^{235}$U, and $^{238}$U. Given element concentrations in kg-element/kg-rock and density $\rho$ in kg/m$^3$, a simplified equation to calculate the present day heat production in a rock is: $$ h \, [\mu \text{W m}^{-3}] = \rho \left( 3.387 \times 10^{-3}\,\text{K} + 0.01139 \,\text{Rb} + 0.04595\,\text{Sm} + 26.18\,\text{Th} + 98.29\,\text{U} \right) $$ The radiogenic heating rate of Earth-like material at Solar System formation was some 10$^3$ to 10$^4$ times greater than present-day values, largely due to decay of $^{26}$Al in the silicate fraction, which was the dominant radiogenic heat source for the first $\sim10$ Ma. Assuming instantaneous Earth formation, the upper bound on radiogenic energy supplied by the most powerful short-lived radionuclide $^{26}$Al ($t_{1/2}$ = 0.7 Ma) is 5.5$\;\times\;$10$^{31}$ J, which is comparable (within a factor of a few) to the planet's gravitational binding energy.