Model dynamo may solve Mercury mystery

Planetary dynamos feed on motion. As molten metal churns in the core, it stretches and bends existing magnetic field lines, thereby inducing additional magnetic field. If the motion were to stop, the planet’s field would decay and vanish. (See the article by Daniel Lathrop and Cary Forest, Physics Today, July 2011, page 40.)

In Earth’s dynamo, core flows are thought to be sustained partly with energy supplied by phase changes at the interface between the solid inner core and the fluid outer core (see figure 1a). As the planet cools, the inner core grows; it incorporates iron and other heavy elements from the outer core and leaves behind a fluid rich in low-density elements such as sulfur. That hot, buoyant fluid rises to the overlying mantle and generates the convective motion that powers the dynamo. (See the article by Peter Olson, Physics Today, November 2013, page 30.)

Traditionally, Mercury’s dynamo has been assumed to operate in similar fashion. But there are reasons to suspect that convective forcing in Mercury’s core may be significantly more complex than it is in Earth’s. For starters, Mercury’s core is thought to contain a much higher concentration of light elements; their depression of the core’s freezing point is currently the only viable explanation for why the relatively small core hasn’t already frozen completely solid. (See Physics Today, July 2007, page 22.)

In 2008 Bin Chen, Jie Li (both then at the University of Illinois at Urbana-Champaign), and Steven Hauck II (Case Western Reserve University, Cleveland, Ohio) showed that when molten iron contains a sufficiently large admixture of sulfur and is compressed to Mercury-like pressures, iron can spontaneously precipitate—even when there’s no solid–liquid interface to seed the phase change.³ They predicted that precipitation could potentially occur in two layers, so-called snow zones, inside Mercury’s core. Sources of heavy precipitates and buoyant light elements, the snow zones (depicted in figure 1b) would further stir the dynamo.

Newer assessments of Mercury’s geochemistry hint at still more complicated forcing patterns. Spectroscopic measurements indicate that Mercury’s silicate surface is poor in iron and rich in sulfur, which suggests that the planet formed under highly reducing chemical conditions. Laboratory experiments mimicking those conditions demonstrate that Mercury’s core likely acquired substantial admixtures of both sulfur and silicon as it formed. If so, the liquid part of the core could consist of two immiscible layers—an iron–sulfur phase and an iron–silicon phase—each of which could spawn snow zones and potentially give rise to other exotic phase behavior.

To see how different forcing patterns influence dynamo-generated magnetic fields, Cao and his coworkers teamed with a numerical modelling group led by Johannes Wicht (Max Planck Institute for Solar System Research, Göttingen, Germany). The researchers didn’t attempt to simulate every possible scenario, just two extreme cases: An Earth-like scenario in which the dynamo is stirred from below and a so-called volumetric buoyancy scenario, which simulates a fully pervasive iron snow. Whereas the Earth-like forcing always yielded a symmetric magnetic field, volumetric buoyancy consistently gave rise to asymmetries similar to that observed for Mercury.

“It’s somewhat counterintuitive, because all of the boundary conditions are symmetric; we don’t know a priori if the system will be stronger in the north or in the south,” says Cao. “But once the system chooses a hemisphere, it stays in that state. It’s a classic example of spontaneous symmetry breaking.”

Planetary dynamos are generally thought to be organized into helical flows along columns aligned parallel to the spin (z) axis. In a typical dynamo, such as Earth’s, the flows in neighboring columns are alternately directed toward and away from the equator, as depicted schematically at the left of figure 2a. (Straight black arrows indicate the axial velocity; curved arrows indicate vorticity, a measure of the fluid’s spinning motion.) In mathematical parlance, the flow configuration is known as an even mode, since the flows in the northern hemisphere mirror those in the south.

Fluid mechanical theory predicts that under strong forcing, dynamos can also host an odd mode, in which fluid travels through the equator, reversing vorticity along the way. Cao and company noticed that although the odd mode itself does not distinguish between northern and southern hemispheres, its superposition with the even mode does. That superposition provides a possible route to magnetic-field asymmetry. Although the precise structure of the magnetic field depends on complex interactions between the three-dimensional flow and preexisting field lines, the field strength correlates roughly with helicity, the dot product of velocity and vorticity. When the odd and even modes overlap, their superposition enhances helicity in one hemisphere and diminishes it in the other. Indeed, that theoretical picture is consistent with helicity profiles obtained in the team’s dynamo simulations, as shown in figure 2b.

The researchers aren’t the first to see symmetry breaking in dynamo simulations. Three years ago, Maylis Landeau and Julien Aubert (both then at the University of Paris Diderot) reported a similar magnetic asymmetry in simulations of the ancient Martian dynamo.⁴ Landeau and Aubert, however, specifically considered the case of a planet with an all-fluid core; the asymmetry resulted from a particular flow mode in which fluid passes through the center of the planet as it travels between poles. Such a mode is plausible for early Mars but not for planets that, like Mercury, have sizeable solid inner cores.

At first glance, the mechanism that Cao and company propose for Mercury’s symmetry breaking seems to contradict previous theoretical studies that predict that the dynamo’s columnar flow structure should destabilize before convective forcing becomes strong enough to excite the odd mode. But those studies assume Earth-like forcing, notes Jonathan Aurnou (UCLA), coauthor of the new paper. “The volumetric buoyancy essentially acts to keep the columns stable.”

Another facet of the team’s model may have been central to symmetry breaking. The researchers tried imposing a variety of boundary conditions for the core’s outer edge, including the customary uniform heat-flux condition and less traditional scenarios in which heat escapes faster near the equator than at mid and high latitudes. Although north–south asymmetries could occur with uniform heat fluxes, the resulting dipoles tended to lie off-center with the spin axis, fluctuate wildly over time, and exhibit a weaker asymmetry than exists on Mercury. When heat was assumed to escape faster near the equators, the fields looked nearly identical to Mercury’s.

To some extent, then, the theoretical explanation of Mercury’s asymmetry hinges on the unproven assumption that the core cools fastest at the equator, probably by way of enhanced convection in the mantle. According to Sean Solomon, principal investigator of the MESSENGER mission, the assumption isn’t too far-fetched. “If there were sustained, enhanced upwelling of the mantle in the equatorial zones—and if that pattern persisted over most of Mercury’s history—then you might expect to see a thicker crust in the equatorial regions. That is, in fact, what we see.”

Solomon cautions, however, that it’s not a given that Mercury’s mantle is convecting at all—much less that it is removing heat fastest near the equator. “Most but not all Mercury models have mantle convection turning off sometime before the present,” he says. “Our ignorance is vast.”