|
|
| Fig. 1: Protoplanetary disk surrounding a new star. (Source: Wikimedia Commons) |
The internal heat of the earth is thought to come primarily from the primordial energy of planetary accretion, frictional heating caused by the segregation and solidification of the earth's core, and the decay of long-lived radioactive isotopes (235U, 238U, 232Th and 40K). However, theories are not in agreement on each of these heat sources' specific contributions to the earth's heat budget. By subtracting any theorized heat generated by radioactive isotopes (radiogenic heat) from the heat budget, the remaining heat from primordial accretion and friction is lost to space and gradually cools the earth. [1]
The earth's macro-composition, pressures, densities, and depths where key boundaries occur, are fairly well understood. This understanding stems from seismic data, the astronomically determined moment of inertia, comparisons with meteorites resembling the early solar system's accretion disk, and laboratory experiments/simulations mimicking deep earth conditions. [2,3] The age and manner of core formation, and the discrepancy between observed and theorized core densities, are not well understood. [2] Differing theories on these matters arrive at differing amounts of heat from the geothermal sources mentioned above. Since humans will likely never be able to drill to the center of the earth due to its extreme conditions, our understanding will only be as good as the agreement between empirical evidence and theory.
Numerous measurement stations within mines and boreholes provide insight into the heat flow from the earth. More accessible or geologically significant areas tend to have more measurements than inaccessible regions such as Antarctica and high-latitude oceans. Modeling based on comparable geologic formation and age is performed for areas not directly measured. By sampling each borehole rock to determine its heat conductivity and multiplying by observed temperatures, heat flow is calculated. The global heat budget is roughly 45 × 1012 W, or 45 TW. [1]
There are numerous theories for how the earth accreted from the protoplanetary disk of material surrounding the new sun (similar to Fig. 1). [3] However, many of them agree that the kinetic energy of impacting accreting bodies was sufficient to heat the earth to a partially or completely molten state. This state continued over the accretion period (~100 million-years) and would have allowed for the differentiation of elements. Liquid Fe gradually sank to the core, attracting certain elements with it, such as Ni, Co, and noble metals. Other elements remained after the sinking of Fe, such as Si, Al, Mg, alkalis, halogens, U and Th. These elements formed a silicate-oxide melt that became the early mantle. [2]
Inner Core: By comparing seismic data with laboratory shock wave experiments, numerous elements show a pressure-density relationship consistent with that of the earth's core. However, Fe is the only sufficiently abundant element in the universe to fit the models. At the core's pressure, density, and assumed temperature, the inner core is generally accepted to be mostly solid Fe. But shock wave models also show that the density of pure Fe at inner core pressures is 8-11% higher than those observed from seismic data. Therefore, other elements must be present. Sulfur is the most likely element to account for the observed density deficit, but that does not preclude the additional presence of O, Si, C, N, MgO, and H. [3]
Studies have subsequently shown that non-Fe attractant alkali metals, such as K, Na, and Rb, can combine with other core-forming metals under high pressures. K, Na, and O were also demonstrated to combine with core-forming metals in the presence of S. [2]
Outer Core: Similar comparisons of seismic data with shock wave experiments help determine the outer core's composition and state. The region between 1220-3480 km from the center does not permit seismic shear waves to propagate. This property confirms a liquid state and thus defines the outer core's dimensions. Also, the outer core's density is too low to be composed of pure Fe at its presumed temperature range. The presence of additional alloying elements, including sulfur, could depress the melting point of Fe, accounting for its lower density and liquid state.[3]
The solidification of the liquid Fe compound at the transition between the inner and outer cores is thought to liberate latent heat and also some of the lighter alloying elements. The combined thermal and compositional buoyancy creates convection in the outer core. The convective motions of this electrically conductive Fe transferring heat to the mantle are thought to have started and maintain the geodynamo which powers the earth's magnetic field. [2]
The earth's dynamo has been in operation for at least 3.5 billion years. This conclusion is inferred by observations of the predominant N-S orientation of Fe-bearing minerals in igneous rocks from that time period. [2] Since there is general acceptance that the geodynamo requires both the liquid outer core and the solid inner core, core separation must have occurred at least that long ago. [4]
Highly reliable Hf-W chronometry allows for further inference of the core's age. Hf preferred to stay with the silicate mantle and W preferred Fe. As 182Hf decayed to 182W with a half-life of 9 million years, it sank into the core. By analyzing both undifferentiated and metallically differentiated meteorites, analogous to core formation, different groups estimated formation to have occurred within 10-60 million years of earth's accretion. [2]
Models of core evolution have difficulty simulating an inner core older than 1 billion years. If the inner core has grown to its current size at a constant rate over the earth's 4.6 billion years, the heat of crystallization (of the liquid outer core solidifying into solid inner core) would provide 0.5 TW. However, estimates of the total core heat flux range from 7-10 TW depending on various assumptions. In the absence of internal heat sources, the difference between the heat flux and heat of crystallization must be accounted for by cooling. The calculated rate of cooling would be 150-200*°K every billion years. This rate is considered too high as it implies a much younger core (conflicting with magnetized samples and Hf-W chronometry), or a much larger inner core (conflicting with seismic date/shock wave comparisons). An additional heat source, such as radiogenic heating, alleviates this conflict. [4]
As mentioned above, K alloys with liquid Fe under high temperature and pressure in the presence of S, and S is a primary candidate to account for the observed density deficit of the core. Accordingly, a K concentration of 250 ppm could be expected in the core, with 40K accounting for 1.7 TW of radiogenic heat from the inner core alone. Again assuming constant inner core growth from crystallization of the outer core, this much heat pushes the age of the core to ~2.5 billion years.
Another study placed the inner core's heat flux at 4 TW, using similar assumptions to those above that estimated the total core heat flux. By altering assumptions about the pressures at which the core and mantle equilibrated, it is possible there is more 40K in the core, or even 235U, 238U, and 232Th. These additional isotopes could account for some of the missing heat and further push back the age of the core. [4]
 |
| Fig. 2: KamLAND Detector Schematic. (Source: Wikimedia Commons) |
Measurements of electron antineutrinos produced in beta decays allow for direct investigation of radioactive isotopes in the mantle. Measurements are made by antineutrino detectors such as Japan's Kamioka Liquid Scintillator Antineutrino Detectors (KamLAND) shown in Fig. 2. In order to interpret detector data, a prediction of the so-called "geoneutrino flux" is needed. Different models analyze seismic wave propagation, meteorites, and igneous rocks to predict the abundances of radioactive isotopes, and thus their geoneutrino flux, in the mantle and crust. Of note, the calculation of radiogenic heat flux from geoneutrino measurement can vary depending on models' accuracy of crust composition, especially in the areas close to the detector (<500 km). Also, current detectors are insensitive to geoneutrinos from the decay of 40K. [5]
One model, Bulk Silicate Earth (BSE), estimates the total heat generated as 20.3 TW in its "middle-Q" (middle-heat) prediction. Of this 20.3 TW, 0.3 TW comes from 235U, 8 TW from 238U, 8 TW from 232Th, and 4 TW from 40K. Comparisons of Japan's KamLAND detector data and Italy's Borexino detector data with the various predictions of the BSE model yield a range of possible radiogenic heat fluxes. Comparisons favor the BSE model's "low- Q" and "middle-Q" predictions, with heat flux estimates ranging from 10-22 TW. The "high-Q" prediction of 25 TW is disfavored by greater than 4σ for either of the BSE model's hypotheses on distributions of U and Th throughout the mantle and crust. [5]
Another theory accounting for the majority of earth's heat is the steady-state planetary reactor. According to the theory, a small sphere of 235U and 238U formed at the center of the inner core, surrounded by Ni-silicide. This arrangement acted like a fast-breeder reactor, creating heat from the fission of U and Pu and driving the geodynamo. [2]
One major criticism of the theory is that U and Th strongly favor silicate formation and thus most likely remained in the mantle and crust during accretion. However, the relative mass of the core is consistent with certain meteorites where U and Th occur alloyed with Fe. One estimate places 64% of the earth's U, enough to start a nuclear reaction, alloyed with Fe- sulfide in the inner core. [2]
The presence of 3He in Hawaiian basalts further backs this theory. Supposedly, these basalts are plume-delivered from the deep mantle and their embedded 3He can originate only as a by-product of nuclear fission and not from primordial gas pockets. This primordial gas supposedly degassed long ago. The basalts' 3He/4He ratio is also distinctly larger than the ratio found in certain sediments, where extraterrestrial dust continuously rains down and is the main source of sediments' 3He. Of note, the basalts' ratio is 34 times larger than the atmospheric ratio. [2]
A final criticism of this theory comes from the KamLAND geoneutrino detector. By adjusting model parameters, detector data put a limit on the planetary reactor at 1.26 TW with a 90% confidence level. Further empirical improvements, such as being able to detect geoneutrinos from the decay of 40K, will be able to further refine understanding of a potential planetary reactor. [5]
The earth's geothermal budget of 45 TW likely comes from energy leftover from accretion, friction from the continual solidification of the core, and radioactive isotopes. Theories of earth's formation vary, which subsequently varies the theorized quantity of radioactive isotopes. Additionally, the extreme difficulty of directly sampling down to the core precludes certainty. However, emerging evidence points to radioactive isotopes contributing some portion to the earth's heat budget. Continued improvements in empirical measurements will further refine scientific agreement on the exact amount of geothermal energy from nuclear decay.
© Peter Slye. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. 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] H. N. Pollack et al., "Heat Flow from the Earth's Interior: Analysis of the Global Data Set," Rev. Geophys. 31, 267 (1993).
[2] A. V. Sankaran, "Recent Concepts About Heat Source from the Earth's Core," Curr. Sci. 83, 932 (2002).
[3] D. J. Stevenson, "Models of the Earth's Core," Science 214, 611 (1981).
[4] J. Brodholt and F. Nimmo, "Core Values," Nature, 418, 489 (2002).
[5] S. Abe et al., "Abundances of Uranium and Thorium Elements in Earth Estimated by Geoneutrino Spectroscopy," Geophys. Res. Lett. 49, e2022GL099566 (2022).
