Radiogenic Heat

Matt Estrada
March 22, 2015

Submitted as coursework for PH241, Stanford University, Winter 2014

Radiogenic heat

How much of the heat dissipated into space by Earth is due to radioactive decay of its elements? About half is due to this "radiogenic heat". That is, about 20 × 1012 Watts of the total ~40 × 1012 W heat flux flowing out from the interior of the Earth is due to Uranium, Thorium, and Potassium radioactively decaying within the its composition, as described in Table 1. It's generally agreed that the rest of the heat is the Earth still cooling down from when it was formed. Were it not for radiogenic heating, the earth's interior would cool at a rate of about 120 K per billion years. The earth's heat budget has tangible effects; mantle convection and tectonics slow down as the Earth cools.

How big of a power source is 20 × 1012 W on a geological scale? In its entirety, radiogenic heat is estimated to have released about 7.6 × 1030 joules over the course of the earth's existence. When the earth was young, radiogenic heating generated about four times as much heat flux as it does now. Still, this amount of heating is dwarfed by the gravitational energy that was released with the formation of the earth. The accretion of a homogeneous mass that comprises the earth and the loss of corresponding gravitational potential energy measures to 219 × 1030 joules. Most of this energy was radiated away during the process, though 13.3 × 1030 joules of residual heat are still stored within the earth [1]. More concisely putting radiogenic heating into perspective, solar radiation onto the surface of Earth accounts for 173,000 × 1012 W [3]. These internal, geological factors are only a small fraction of the earth's total energy budget.

Isotope μW/kg of Isotope μW/kg of Element Estimated Total Earth Content (kg)
238U 95.0 94.35 12.86 × 1016
232Th 26.6 26.6 479 × 1016
40K 30.0 0.00350 7.77 × 1020
Table 1: Thermally important radioactive elements in the Earth. [1]

Geoneutrino Measurements

Measurements to deduce the amount the radioactive decay within the Earth have been conducted utilizing geoneutrino measurements. A geoneutrino is an electron antineutrino emitted in β - decay of any radionuclide found in the Earth. Since neutrinos only interact through the weak force, the earth is transparent to them. Put simply, geoneutrinos offer a direct window to view reactions on the interior of the earth.

Measurements taken at the Kamioka Liquid-Scintillator Antineutrino Detector over a seven-year period starting in 2002 offer the most comprehensive dataset thus far. The detector is built under Mount Ikenoyama in Japan. The mountain provides an effective overburden of 2,7000m of water equivalent. This reduces the cosmic-ray-induced muon flux to 5.37 ± 0.41 m-2h-1 and thus ensures the remaining, registered events originate from the earth.

Accurately mapping neutrino sources requires data from multiple sites; thus the calculations here included measurements taken from the Borexino detector in Italy [5]. The measurements taken at KamLAND account for less than 10% of the expected geoneutrino flux from the earth. The site measured the number of recorded geoneutrino events and compared them against models on the number of expected hits. Using these geological models, the radiogenic heat from 238U and 232Th was estimated to be 19.9 ± 9.2 × 1012 W to a 96.6% confidence level [2]. The neutrinos emitted from 40K are below the level of detection of these experiments, but are known to contribute 4 TW. All this is part of a determined heat-loss rate of 46 ± 3 × 1012 W from the planet [4].

© Matt Estrada. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] F. D. Stacey and . M. Davis et al., Physics of the Earth (Wiley, 2008).

[2] A. Gando et al. "Partial Radiogenic Heat Model for Earth Revealed by Geoneutrino Measurements", Nat. Geosci. 4, 647 (2011).

[3] D. Archer, Global Warming: Understanding the Forecast (Wiley, 2011).

[4] C. Jaupart, S. Labrosse, and J.-C. Mareschal, "Temperatures, Heat and Energy in the Mantle of the Earth," in Treatise on Geophysics, Vol. 7, ed. by G. Schubert (Elsevier, 2007), p. 253.

[5] G. Alimonti et al., "The Borexino Detector at the Laboratori Nazionali del Gran Sasso," Nucl. Instrum. Methods A 600, 568 (2009).