Did lunar tides sustain the early Earth's dynamo?

Abstract

Geological data show that, early in its history, the Earth had a large-scale magnetic field with an amplitude comparable to the one of the present geomagnetic field. However, its origin remains enigmatic and various mechanisms have been proposed to explain the Earth's field over geological time scales. Here, we critically evaluate whether tidal forcing could explain the ancient geodynamo, by combining constraints from geophysical models of the Earth-Moon system and predictions from turbulence studies. Our analysis shows that lunar tidal forcing could have been sufficiently strong before $-3.25$ Gy to trigger turbulence within the Earth's core, and potentially to sustain dynamo action during that interval. Then, we propose new scaling laws for the magnetic field amplitude $B$. We expect the latter to scale as $B \propto β^{4/3}$, where $β$ is the equatorial ellipticity of the liquid core, if the turbulence involves weak interactions of three-dimensional inertial waves. Alternatively, in the regime of strong tidal forcing, the expected scaling becomes $B \propto β$. When extrapolated to the Earth's core, it suggests that tidal forcing alone was too weak to possibly explain the ancient geomagnetic field. Therefore, our study indirectly favours another origin for the early Earth's dynamo on long time scales (e.g. exsolution of light elements atop the core, or thermal convection due to secular cooling).

Figures (14)

• Figure 1: Paleointensity at the Earth's surface during the Hadean and Archean periods. Measurements have been performed on either single-silicate crystals (e.g. zircons) or whole rocks (e.g. Banded Iron Formations). Data from the pint database bono2022pint and nichols2024possible. Geological eons are also shown (H: Hadean, A: Archean).
• Figure 2: Sketch (not to scale) of the elliptical geometry of the tidally deformed Earth's core, as seen the orbital plane of the Moon. $R_s$ is the mean surface radius, and $R_\text{cmb}$ is the mean core radius. The radial displacement along the major axis in the equatorial plane is $s_\mathrm{max}$, and that along the minor axis is given by $s_\mathrm{min} = -s_\mathrm{max}/2$ for a tidal potential of degree $2$.
• Figure 3: Maximum radial displacement $s_\mathrm{max}$ and inverse polar flattening $f^{-1}$ at present day, as a function of normalised mean radius $r/R_s$, as computed for tidal theory and hydrostatic equilibrium theory. In both cases, the same Earth's reference model is chosen dziewonski1981preliminary. Red region shows the solid inner core, and grey one the liquid outer core.
• Figure 4: Comparison between geologic data and models for the evolution of the normalised Earth-Moon distance $a_M/R_s$ in (a), and of the length of day in (b). Insets show the age $\tau$ between $-1$ and $-0.1$ Gy. $R_s \simeq 6378$ km is the mean value of the Earth's radius. Orbital model: farhat2022resonant. Paleontological data: williams2000geological and references therein. Cyclostratigraphic data: zhou2024earth and references therein. Tidal rhythmites data: farhat2022resonanteulenfeld2023constraints and references therein.
• Figure 5: Evolution of the Earth's core ellipticity $\beta$, polar flattening $f$, and of $\Omega_\text{orb}/\Omega_s$, as a function of age. Dashed line shows the frequency value associated with the least-damped mode in resonance condition (\ref{['eq:resonancecondition']}). Geological eons are also shown (H: Hadean, A: Archean, P: Proterozoic).