The Sun, as They Might Be Giants taught us, is a mass of incandescent gas, mostly in the form of hydrogen plasma. And its poles are moving slower than its equator: The equator spins once every 24.5 days, whereas the polar regions rotate once every 35 days.
Researchers have precisely measured this phenomenon, known as differential rotation, using the flow of plasma in the Sun’s outer layers, but theoretical understanding of why it occurs has been lacking.
“We don’t fully understand differential rotation, and numerical models are not able to reproduce it from first principles,” said Laurent Gizon, a solar physicist at the Max Planck Institute for Solar System Research in Göttingen, Germany.
Initially, researchers reasonably assumed that the poles would spin faster than the equator, much as a figure skater spins faster when their arms are pulled in. But the Sun’s rotation behaves the opposite way. More advanced fluid dynamics models can explain the speedier equatorial region but predict a greater pole-to-equator speed difference than the Sun experiences.
Gizon and his colleagues have proposed a possible explanation: relatively slow moving spiral waves concentrated at high latitudes that carry heat from the poles to the equator. According to their theoretical model, these so-called inertial modes even out conditions in the convection zone, the region directly beneath the solar surface, which in turn levels out the difference in rotational speed across the entire Sun. The researchers published their analysis in Science Advances.
Below the Surface
A major reason to study differential rotation is its connection to the solar dynamo, which governs the 11-year cycle of magnetic tangling behind sunspot activity and solar storms.
“About 98% of solar physicists are dermatologists, who study the skin of the Sun,” said Mark Miesch, a solar physicist at the University of Colorado Boulder who was not involved in this project.
Understanding differential rotation involves looking at the Sun’s interior, which can be done with helioseismology—observing and modeling sound waves moving through the convection zone. These vibrations reveal information about the internal structure of our star, much as earthquakes do for Earth, and can be mapped using ground-based observatories such as the Global Oscillation Network Group (GONG) or spacecraft such as NASA’s Solar Dynamics Observatory (SDO).
“It’s very important to have a longer observation window to follow these [inertial modes] as long as possible.”
Gizon and colleagues used data from these observatories to take a fresh look at the problem of differential rotation. Their data span 2017–2021, when the Sun’s magnetic activity was near its lowest, which reduced the complications that the Sun’s magnetic fields pose on modeling efforts. Looking over periods longer than those typically examined in helioseismology also allowed them to isolate the inertial modes from any magnetic effects.
The slow-moving waves in their model swirl at speeds between 1.1 and 3.8 meters per second (2.5 to 8.5 miles per hour)—comparable to human walking or running speeds and far smaller than the dramatic sound waves that dominate helioseismic data.
At high latitudes, the inertial modes form spirals of plasma, with the “arms” of the spirals curling in the direction of rotation. Modeling all of this required a 3D mathematical treatment to include convection zone behavior, along with latitudinal and meridional flows.
“It’s very important to have a longer observation window to follow these [inertial modes] as long as possible,” Gizon said, adding that these sound waves are also very large wavelength in a spatial sense, which adds to the difficulty in identifying them. “We need many years of data in order to establish that we’re looking at a global mode of oscillation.”
Seven Degrees of Separation
For Gizon and colleagues, the twisty nature of the inertial modes was a sign of an underlying instability in the plasma, similar to atmospheric instabilities such as polar vortices on Earth that drive weather patterns.
Their model reproduces the inertial modes, showing how they drive plasma from the hotter poles toward the cooler equator. This action evens out the temperature within the convection zone, predicting that the total temperature variation can’t exceed 7 kelvin (which is minuscule compared to the background temperature of about 2 million kelvin). That additional plasma flow changes the internal temperature profile of the Sun and results in the observed differential rotation.
Miesch described the process as a kind of negative feedback loop that both drives the flow of plasma and keeps the temperature inside the convection zone almost uniform from equator to pole.
“The idea that instabilities can limit the temperature gradient, I think is a good one, and it’s a novel idea.”
“The idea that instabilities can limit the temperature gradient, I think is a good one, and it’s a novel idea,” Miesch said.
However, the current version of the theory doesn’t include magnetic fields, which Miesch said worries him. In a sense the current model works too well he said, thanks to the authors’ choice of parameters. If adding magnetic fields to the model wipes out the temperature gradient—and the differential rotation—that calls the parameterization into question and raises concerns that the model could be simply adjusted to make things work again.
Though that issue doesn’t necessarily mean the theory is wrong, it does mean more work is likely necessary to check the results against observation when the full complexity of the Sun is taken into account. In particular, Gizon is looking forward to the next generation of helioseismology spacecraft, which will be able to probe high-latitude solar regions in higher detail.
“We need to understand inertial modes to understand what they are sensitive to,” he said. “Then we need to connect the measurements to the models.”
—Matthew R. Francis (@DrMRFrancis), Science Writer