Long-period oscillations control the Sun’s differential rotation

High-latitude long-period oscillations provide a feedback mechanism that limits the Sun’s pole-to-equator differential rotation.

March 27, 2024

The interior of the Sun does not rotate at the same rate at all latitudes. The physical origin of this differential rotation is not fully understood. A team of scientists at the Max Planck Institute for Solar System Research (MPS) in Germany has made a ground-breaking discovery. As the team reports today in the journal Science Advances, the long-period solar oscillations discovered by MPS scientists in 2021 play a crucial role in controlling the Sun’s rotational pattern. The long-period oscillations are analogous to the baroclinically unstable waves in Earth’s atmosphere that shape the weather. In the Sun, these oscillations carry heat from the slightly hotter poles to the slightly cooler equator. To obtain their new results, the scientists interpreted observations from NASA’s Solar Dynamics Observatory using cutting-edge numerical simulations of the solar interior. They found that the difference in temperature between the poles and the equator is about seven degrees.

The Sun’s differential rotation pattern has puzzled scientists for decades: while the poles rotate with a period of approximately 34 days, mid-latitudes rotate faster and the equatorial region requires only approximately 24 days for a full rotation. In addition, in past years advances in helioseismology, i.e. probing the solar interior with the help of solar acoustic waves, have established that this rotational profile is nearly constant throughout the entire convection zone. This layer of the Sun stretches from a depth of approximately 200 000 kilometers to the visible solar surface and is home to violent upheavals of hot plasma which play a crucial role in driving solar magnetism and activity.

While theoretical models have long postulated a slight temperature difference between solar poles and equator to maintain the Sun’s rotational pattern, it has proven notoriously difficult to measure. After all, observations have to “look through” the background of the Sun’s deep interior which measures up to million degrees in temperature. However, as the researchers from MPS show, it is now possible to determine the temperature difference from the observations of the long-period oscillations of the Sun.

Longitudinal velocity pattern in the simulation

A spiraling flow pattern at high latitudes seen at the surface penetrates deeper into the Sun’s whole convection zone.

High-latitude oscillations control differential rotation

In their analysis of observational data obtained by the Helioseismic and Magnetic Imager (HMI) onboard NASA’s Solar Dynamics Observatory from 2017 to 2021, the scientists turned to global solar oscillations with long periods that can be discerned as swirling motions at the solar surface. Scientists from MPS reported their discovery of these inertial oscillations three years ago. Among these observed modes, the high-latitude modes with velocities of up to 70 km per hour, proved to be especially influential.

To study the nonlinear nature of these high-latitude oscillations, a set of three-dimensional numerical simulations was conducted. In their simulations, the high-latitude oscillations carry heat from the solar poles to the equator, which limits the temperature difference between the Sun’s poles and the equator to less than seven degrees. “This very small temperature difference between the poles and the equator controls the angular momentum balance in the Sun and thus is an important feedback mechanism for the Sun’s global dynamics” says MPS Director Prof. Dr. Laurent Gizon.

In their simulations, the researchers for the first time described the crucial processes in a fully three-dimensional model. Former endeavors had been limited to two-dimensional approaches that assumed the symmetry about the Sun’s rotation axis. “Matching the nonlinear simulations to the observations allowed us to understand the physics of the long-period oscillations and their role in controlling the Sun’s differential rotation”, says MPS postdoc and the lead author of the study, Dr. Yuto Bekki.

Comparison between solar observations and nonlinear simulations

The left column shows the observed velocity eigenfunction of the m=1 high-latitude mode and the internal rotational profile of the Sun measured by global helioseismology. The middle column shows the simulation counterparts. The right panels show the simulated amplitudes of the m=1 mode and the latitudinal differential rotation as functions of the pole-to-equator temperature difference.

Solar interior and Earth atmosphere share similar physics

The solar high-latitude oscillations are driven by a temperature gradient in a similar way to extratropical cyclones on the Earth. The physics is similar, though the details are different: “In the Sun, the solar pole is about seven degrees hotter than equator and this is enough to drive flows of about 70 kilometers per hour over a large fraction of the Sun. The process is somewhat similar to the driving of cyclones”, says MPS scientist Dr. Robert Cameron.

Great expectations

Probing the physics of the Sun’s deep interior is difficult. This study is important as it shows that the long-period oscillations of the Sun are not only useful probes of the solar interior, but that they play an active role in the way the Sun works. Future work, which will be carried out in the context of the ERC Synergy Grant WHOLESUN and the DFG Collaborative Research Center 1456 Mathematics of Experiments, will be aimed at better understanding the role of these oscillations and their diagnostic potential.


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