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Simulations Uncover Surprises in Sun’s Turbulent Interior

TACKLING TURBULENCE
DIFFERENTIAL ROTATION


he Sun regularly reminds us that we are at its mercy. Recurring sunspots, erupting solar flares, and coronal mass ejections spew hot plasma into space, often flooding the Earth with high-energy particles. When the Sun is magnetically active, its outbursts can disrupt satellite communications and knock out power grids. “One of the great puzzles in nature has been why the Sun has 22-year cycles of magnetic activity,” said Juri Toomre, a professor in JILA (formerly called the Joint Institute for Laboratory Astrophysics) and the Department of Astrophysical and Planetary Science at the University of Colorado, Boulder. Trying to sort out the Sun’s magnetic mechanism requires charting the turbulent flows at various depths and latitudes, using both theoretical models and deductions based on helioseismic data.

Figure 1: Modeling Solar Convection
(Nic Brummell, Juri Toomre)

Figure 2: Layers of Turbulence
Just beneath the surface of our closest star lies a deep shell of raging turbulence. Hot gases erupt upward and plummet downward while being contorted by rotation and shear. Such complex flows within this shell, which occupies the outer 30 percent of the Sun, lead to a striking differential rotation—at the solar surface, equatorial regions rotate once in about 25 days and the poles in about 33 days. Helioseismology, the study of acoustic waves of the deep interior that are detectable at the surface, has revealed that such differential rotation cuts down through the layer, terminating at the base of the convection zone in a shear layer called the tachocline.

The differential rotation is thought to have a crucial role in the Sun’s ability to build magnetic fields by dynamo processes. Toomre and his colleagues at the University of Colorado have been generating 3-D models of the solar convection zone to understand the physics that link turbulent convection, rotation, and magnetism.

“The solar differential rotation and magnetism raise difficult questions, the resolution of which requires focused and sustained simulation efforts,” said Toomre. In particular, he and his group are interested in the convection zone of intense turbulence, and in the tachocline of shear that separates it from the deeper radiative interior. The tachocline is the most likely location of the “solar dynamo,” essentially an enormous factory that builds and regulates the magnetic fields of the Sun. Recent helioseismic studies have shown that there are repetitive speedups and slowdowns of rotation rate above and below the tachocline with a period of about 1.4 years. This discovery of a solar “heartbeat” most likely arises from the dynamo.

TACKLING TURBULENCE

Toomre and his colleagues create computational models that can be compared to the results of seismic probing of the solar interior. They have developed an approach for simulating turbulent convection that involves two codes, an anelastic spherical harmonic (ASH) code and a hybrid pseudo-spectral (HPS) code. The ASH code generates a global picture of the dynamics of convection, rotation, and magnetism within a full spherical shell, while HPS simulates a higher-resolution, localized planar domain within that shell. Recently, the group made significant gains in optimizing the two codes—both performing efficiently on scalable parallel architectures, including NPACI’s Blue Horizon supercomputer at SDSC.

“The two approaches provide information that adds up to a more complete picture,” said Nic Brummell, assistant professor at the University of Colorado. “HPS extracts a small piece of the sphere, allowing for a much higher degree of turbulence. ASH models a full shell with the correct geometry.”

Brummell and Toomre have used HPS to compute what happens to an unstable layer of fluid when a stable layer sits below it, mimicking the conditions at the base of a stellar convective envelope. The simulation allows the researchers to peer beneath the smooth surface to the boiling turbulence below (Figure 1).

In a paper accepted for publication by the Astrophysical Journal, Brummell and Toomre report that turbulent plumes originating from the convection zone bore into the stable radiative zone beneath it. This leads to transport of material and magnetic fields from one layer into another. Adding rotation to the system decreased the penetration by deflecting some of the plumes’ energy into horizontal mixing. Further, the interaction studied here between the highly turbulent interior and the rotation has provided insight into the disparity of helioseismic and early numerical results for the differential rotation.

“We now have access to sufficient resolution to study convective turbulence as opposed to laminar or mildly turbulent flows,” Brummell said. HPS ran on the Cray T3E and now runs on Blue Horizon. “These simulations have led to an understanding of mechanisms that are essential to the solar global dynamo. For example, the overshooting turbulent plumes can remove magnetic fields from the convection zone and deposit them in the tachocline.”

DIFFERENTIAL ROTATION

Toomre and Sacha Brun, a postdoctoral researcher at JILA, follow a second approach to investigating solar convection, using the ASH code to generate a global model of how rotation influences turbulent convection within a full spherical shell. This provides information that cannot be detected in the localized domains studied with HPS, such as global properties of differential rotation. Using ASH, they have created a series of 3-D simulations, each incorporating more turbulence than the last. With every increase, the patterns of convection changed, with larger banana-shaped areas of convection giving way to more frequent and stronger vortices. In addition, they examined the turbulence at different depths in the models, peeling back layers of the Sun to examine how structures related to turbulence spread through the convection zone. They found that networks of relatively persistent downflows sink deep into the unstable layer, providing a mechanism for the redistribution of angular momentum (Figure 2).

Brun said that “using our global ASH code on teraflops computers like Blue Horizon allows us to perform numerical experiments that are beginning to capture the richness of turbulent dynamics and magnetism within our nearest star.”

In another paper accepted for publication by the Astrophysical Journal, Toomre and Brun report that their simulations of turbulent convection under the influence of rotation closely match helioseismic pictures of the differential rotation within the bulk of the convection zone. They investigated factors such as the Reynolds stresses in transporting angular momentum toward the Sun’s equator to create the differential rotation. In studies that are just now becoming computationally feasible, Toomre and his colleagues hope to use ASH to investigate problems such as the role of shear at the edges of the convection zone.

“The solar turbulent convection zone has striking dynamical properties that continue to challenge basic theory,” said Toomre. Despite those challenges, such dual computational approaches for investigating solar convection is providing evidence that matches and explains solar observations.

“A novel aspect of our research is that we are able to test and evaluate the result of the simulations by turning to ongoing helioseismic observations and their deductions about dynamics deep within the Sun for both guidance and inspiration,” said Toomre. —CF


PRINCIPAL INVESTIGATOR
Juri Toomre
JILA, University of Colorado, Boulder

COLLABORATORS
Nic Brummell, Sacha Brun, Marc DeRosa, Kelly Cline
University of Colorado, Boulder

Tom Clune
SGI

Laura Carrington,
Stuart Johnson
SDSC

Mark Miesch
High Altitude Observatory, NCAR