Did lunar tides sustain the early Earth’s dynamo?

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 $B propto eta^{4/3}$, where $eta$ 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 $B propto eta$. 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).