Science has enabled humans to travel into space and walk on the moon. The Voyager satellites have given us new insight into the distant planets Jupiter and Neptune. However, there is still much that is not known about the Sun, particularly the physics of the interior of this star.

The upper layers of the Sun consist of hot plasma, flowing in swirling currents of ionized gases and creating a complex pattern of magnetic fields. This process is called magnetohydrodynamic (MHD) convection. Since the inside of the sun cannot be directly observed and is of too large a scale for experiments to yield effective results, modeling and simulating on supercomputers present the only feasible approach to studying the solar convection zone.

Knowledge about the dynamic behavior of magnetic fields is imperative to understanding observed solar phenomena such as solar flares. Steve Lantz, a member of the Computational Science and Engineering Group (CSERG) at the Cornell Theory Center, has developed both numerical and theoretical models that may help us better understand this complex process. By integrating the fields of astrophysics, fluid mechanics, and numerical analysis, and by using the computing resources available at the Center, Lantz simulated a small slice of the sun's convective layer. As a mentor for the Center's Supercomputer Program for Undergraduate Research (SPUR), he was able to involve Michael Wiltberger, an undergraduate student at Clarkson University, in the process of visualizing his results, as part of Wiltberger's summer experience.

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A fluid can be defined as a large collection of interacting particles whose overall properties evolve over time when acted upon by various forces, such as gravity and friction. Using electromagnetic theory, along with special approximations to the fluid-mechanics equations, Lantz developed a set of rules governing the behavior a solar-like fluid prone to developing convection currents. He also developed an abbreviated system of MHD equations which similarly takes into consideration the conductivity and viscosity of the fluid, as well as gravitational effects and how the fluid is affected by changes in temperature and magnetic fields.

Lantz's rules give a simplified model of fully-resolved simulations of MHD convection, which is helpful in understanding the results. The data obtained from solving these simplified equations compared favorably with data sets from the more complex supercomputer simulations. The sizes of the simplified solutions ranged from single data points for steady states, to a few thousand data points for the largest cycle.

The solutions to Lantz's system of equations were generated using a software package for integrating ordinary differential equations developed at Cornell's Center for Applied Mathematics. Wiltberger reconstructed, rendered, and animated streamlines and magnetic field lines resulting from the dynamics of the convection process with a "flip book" tool developed by visualization specialist Wayne Lytle. The final length of the animation is approximately eleven minutes.

The video illustrates how magnetic fields can be transported from the interior of the sun to its photosphere, captures steady magnetic fields on the solar surface, and even portrays occasional eruptions, typical on the ever-changing face of the sun. These phenomena are illustrated as animated contour plots that show the motion of the fluid and the movement of the magnetic field lines. The complex dynamics are then illustrated by appealing to examples from the simplified model, as rendered by Wiltberger.

Lantz's research may eventually help enhance understanding of the motion of solar magnetic fields and sunspots. His model can also generally describe the motion of two-dimensional heated and electrically conductive fluids in the presence of magnetic fields which can be found inside stars other than the Sun. Insights gained through visual analysis of the models' results could thus lead to better understanding of the physics within the convective layers of different stars.

Lantz intends to expand his work to study the effects of the Sun's rotation on the internal convective motion of the plasma. Working with Lantz, Wiltberger had the opportunity to contribute to leading-edge research and to see firsthand how the visualization of the results of scientific equations can lead to the better understanding of complex numerical data sets.

Steven R. Lantz

(Click for cover shot).......Last updated February 1994