Understanding Young Earth’s Dynamo
About 4.5 billion years ago, a Mars-sized planet slammed into Earth. The impact remade Earth, created the Moon, and turned both bodies into spinning balls of molten rock. A billion years later, Earth and its Moon each gained a solid crust and a magnetic field. Although the Moon’s magnetic field fizzled out long ago, Earth’s retains its original strength. The broad reasons for that longevity were recognized decades ago. However, a detailed model of the dynamo’s past, present, and future remains elusive because the churning of the planet’s liquid core that drives the dynamo is so turbulent. Now Yufeng Lin of Southern University of Science and Technology in China and his collaborators have used 2500 CPU years of computer time to simulate Earth’s dynamo before the planet’s inner core began to solidify 1–1.5 billion years ago [1]. The magnetic-field configurations that emerged from the simulations are consistent with those inferred from ancient rocks, solving the mystery of how young Earth sustained a dynamo.
To possess a dynamo, a planet must have an electrically conducting liquid core and a way to stir it. In Earth’s case, stirring is powered by the core’s thermal energy and by the decay of radioactive elements in the core. The stirring itself can come from two sources of convection. At the bottom of the mantle surrounding the liquid, outer core, magma becomes depleted of oxygen, silicon, and other light elements. The magma detaches from the mantle and sinks into the outer core. Above the inner core, a continuously crystallizing mix of iron and nickel expels lighter elements, which float upward through the outer core.
Geophysicists quantify the extent to which a dynamo persists or vanishes through the value of the magnetic Reynolds number (Rm), defined as the ratio of the time electrical currents take to dissipate to the time the liquid core takes to circulate. If Rm exceeds 40, a dynamo is sustainable. Earth’s Rm is reckoned to be about 1000, as expected for a long-lived dynamo. Another key parameter is the Ekman number (Ek), the ratio of the viscous force to the Coriolis force. Ek is reckoned to be about 10–15 for Earth’s liquid core. The extremely low value reflects the molten metal’s low viscosity, which makes the fluid highly turbulent and thus taxing to model.
Measurements of old rocks and models of Earth’s thermal history indicate that the planet had a dynamo well before the inner core began to solidify. Dynamo simulations, however, typically assume a solid inner core, in part because it’s a source of convective stirring. Aiming to recreate the dynamo of young Earth, Lin and his collaborators modeled the core as a liquid contained in a rotating sphere, a choice that entailed resolving some mathematical singularities (derivatives that would otherwise diverge at zero radius). The requisite stirring in their model originated from a temperature gradient imposed across the sphere–mantle boundary. They used Navier-Stokes and Maxwell equations to describe the system’s magnetohydrodynamics.
The simulated dynamo quickly established itself and settled into stable state with an Rm of 500. Lin and his collaborators ran simulations at three different values of Ek: 10–6, 10–7, and 10–8, the last being the smallest Ek any simulation has ever reached. Although 10–8 is 7 orders of magnitude larger than the true value, the researchers found that the dynamo’s magnetic energy, kinetic energy, Rm, and other quantities had lost their dependence on Ek. The finding is a relief for modelers, as it suggests that precious computing power need not be spent coping with the fluid core’s extremely low viscosity.
Lin and his collaborators used their model to generate maps of Earth’s magnetic field at the planet’s surface. The simulated field’s variations in intensity and morphology resembled those inferred from measurements of rocks from the Precambrian—the earliest era of Earth’s life. Surprisingly, the simulated maps also resembled ones generated by CHAOS-7, a geomagnetic-field model of Earth’s current magnetic field that incorporates space- and ground-based measurements.
Does the resemblance between the modeled past and the measured present imply that the inner core is not required to sustain Earth’s dynamo? Not necessarily, says Lin. Evidence is strong that the buoyancy that arises from the solidification of the inner core helps to drive the present-day magnetic field. But the addition of an inner core turns the vessel that contains the molten metal from a sphere into a shell. “What we show is that the geometry is probably not [as] important as previously thought, as long as there are sufficient energy sources to drive convection in the Earth’s core,” he says.
“I feel this is an extremely important paper on two fronts,” says Harvard University geophysicist Jeremy Bloxham. He points out that the work provides numerical evidence to back up the view, derived from paleomagnetic data, that Earth’s magnetic field was quite similar to today’s field long before the emergence of the inner core. “In addition, the numerics—achieving the asymptotic regime of small viscosity—is a major step forward,” he says.
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- Y. Lin et al., “Invariance of dynamo action in an early-Earth model,” Nature 644, 109 (2025).