Nonlinear Force-Free Field Modeling AIA/HMI Science Team Meeting Session C2 14 February 2006 Marc DeRosa on behalf of the “NLFFF Consortium” (Karel Schrijver, Marc DeRosa, Tom Metcalf, Yang Liu, Jim McTiernan, Zoran Mikic, Stéphane Régnier, Gherardo Valori, Mike Wheatland, Thomas Wiegelmann)

Rationale Understanding the conditions under which solar magnetic fields can destabilize to erupt in flares and coronal mass ejections requires a quantitative understanding of the coronal magnetic field and currents. HMI will provide measurements of the vector magnetic field at the photosphere. Thus, we seek a method that models the coronal field using photospheric data as boundary conditions.

The Plan The problem: We wish to find B such that  ·B=0 and (∇×B)×B=0 in a closed volume subject to a set of boundary conditions. We compared several classes of methods on pixel test cases for which the solution was known (Schrijver, et al., 2006, SPh in press). The method classes are: Grad-Rubin- based, optimization, Green-function-based, and stress-and-relax (magnetofrictional).

Results so far…

The best method seems to be the optimization method, in which the goal is to minimize the following function: The method is best in terms of both closeness to the known result, as well as computational speed. But… there are issues…

Conclusions (vis-à-vis SDO) In its present implementation, the optimization method will be slow for input data from SDO. Current pixel boxes require ~10 minutes on small numbers of CPUs. However, problem size scaling goes at least as n 4. The photosphere is not force free, and so extrapolations using photospheric boundary conditions contain this additional source of uncertainty. We plan to use loop features visible in Hα and various EUV channels as additional constraints. We are still working on its implementation, and suitable automated loop tracing algorithms are not available yet. Additional investments in resources are needed to deal with the above problems in order for NLFFF models at high resolution and fast cadences to become a regularly computed data product for community-wide use.