In the late 1980s, scientists realized they could understand the interior properties of the Sun by observing the sound waves that resonate inside it. This technique, called helioseismology, revealed a mysteriously thin dynamical layer in the interior of the Sun that became known as the tachocline.
The tachocline is extremely thin but has been believed to play a major role in driving the magnetic properties of the Sun. For years, scientists have theorized, calculated, and modeled these layers of the Sun, but the question of the dynamics that lead to the existence of the tachocline has remained an extremely complicated mathematical puzzle.
Now, researchers at the University of California, Santa Cruz, have produced the first self-consistent models of the Sun’s interior that incorporate the appropriate dynamics and spontaneously produce a tachocline, marking a major step forward for solar physics. Their models were produced using NASA’s most powerful supercomputer, and results are published in a study in The Astrophysical Journal Letters.
For us on Earth, the tachocline is important because of its expected role in producing the Sun’s magnetic fields. These fields trigger events like solar flares and coronal mass ejections—outbursts of activity from the Sun which can devastate global power grids and disrupt our satellites. Reliably predicting when these events will occur requires modeling the solar interior accurately, especially the tachocline.
Farther from home, insights into the properties of our Sun’s tachocline could provide insight into the magnetic activity of other stars. Scientists believe that the magnetic properties of a star may be crucial to its capacity to host other planets that sustain life.
“We know a lot of information about the Sun, but the Sun is just one star,” said Loren Matilsky, a postdoctoral scholar at UC Santa Cruz and the study’s first author. “We’re learning a lot about our Sun’s dynamics, and in the process, I think we’re also learning about how this works on other stars. The questions of the tachocline become all the more important in light of other stellar systems and exoplanets.”
Extremely thin
Matilsky, his mentor Nicholas Brummell, professor of applied mathematics at the Baskin School of Engineering, and former UC Santa Cruz graduate student Lydia Korre, who is now a researcher at the University of Colorado Boulder, pursued this research on the tachocline as part of the NASA-funded Consequences of Fields and Flows in the Interior and Exterior of the Sun (COFFIES) DRIVE Science Center. This large multi-institutional group, of which UC Santa Cruz is a significant part, seeks to understand the solar “dynamo,” which is the physical process that creates the sun’s magnetic fields.
The tachocline plays a major role in the solar dynamo in that it separates two distinct regions of the Sun. Below the tachocline is the radiative zone, which is the innermost 70% of the Sun by radius and rotates rigidly in the way a solid baseball does. Above the tachocline lies the convective zone, the outermost 30% of the Sun by radius, which rotates differentially with the characteristic fluidity of a gas. Between these two zones lies the extremely thin tachocline, whose large variations in velocity likely play a key role in the dynamo.
“Looking at the dynamics initially, you would not expect the tachocline to be that thin because there are multiple processes that would tend to spread the tachocline if left to their own devices— so a big mystery is always ‘why is it that very, very narrow layer?’” Brummell said.
For years, researchers have been attempting to solve the mathematical equations of magnetic fluid dynamics for the solar geometry to confirm the predictions and models surrounding the tachocline.
But the Sun is a very powerful and turbulent ball of a gas, which means that there is a massive range of scales having to do with its motions, from the very tiny (say, 10 meters) to the very large (say, one million kilometers). Similarly, there is a huge range of relevant time scales. This makes the Sun extremely difficult to model, and past attempts have not been able to reproduce the essential realistic dynamical processes at work in the solar interior.
‘Hero’ calculations
Despite these difficulties, Matilsky, in his own words, “welcomes a good challenge.” He and Korre took on the massive task of producing “hero” calculations—extremely complex and large mathematical simulations—that more accurately modeled the physical processes at work in a solar-like parameter regime.
Past attempts at modeling the Sun have struggled to correctly prioritize the physical processes that influence the solar dynamo. This is again because of the huge range of length and time scales that these processes span. In this work, for the first time, the team was able to invest the computational resources necessary to achieve the correct ordering of the dynamics. Their models favor a process called “radiative spreading,” which tends to make the tachocline thicker over time, over another thickening process believed to be negligible in the Sun called “viscous spreading.”
“Loren and Lydia have been doing very painful, big simulations, where we make the simulations big enough and difficult enough so that we could deprioritize viscosity in favor of the much more realistic radiative spreading process,” Brummell said.
When running their re-prioritized models, using NASA Ames’ Pleiades supercomputer for tens of millions of supercomputing hours over 15 months to power their simulations, they were able to create, for the first time, a fully self-consistent model of how the tachocline works. Without prompting it to specifically do so, their models of the convective and radiative zones spontaneously produced a tachocline. Interestingly, it was the forces produced by the dynamo running in the convective zone that were the key to maintaining the thinness of the tachocline in this model.
“There’s a synergy here, because the tachocline is believed to play a fundamental role in causing the dynamo process. It now seems that the reverse may also be true, in the sense that the magnetic field from the dynamo may cause the tachocline to exist in the first place,” Matilsky said.
This research was supported by NASA and the National Science Foundation (NSF) through the COFFIES DRIVE Center, with funding from additional NASA and NSF grants.