Considerations on using Solar-B observations to model the coronal field over active regions Karel Schrijver, Marc DeRosa, Ted Tarbell SOT-17 Science Meeting; 19 April 2006

Field modeling methods Comparison of 6 non-linear force free-field models reveals: Analytical test cases can be successfully modeled. Solutions are very sensitive to boundary conditions (which reflect the field in the [distant] surroundings of a region), as well as to errors in the vector field of the strong-field regions. Owing to this, models should not be expected to match high, weak fields. Convergence is sensitive to initial field configuration. Models differ by a factor of one million in CPU time per step. Best-performing model: the Wheatland et al. (2000) optimization method as implemented by Wiegelmann (2004). See: Schrijver et al., SPh 2006, in press; “Non-linear force-free modeling of coronal magnetic fields. I. A quantitative comparison of methods. URL:

Computational requirements Best current model requires ~8,000 CPU hrs for a 1024x1024x128-pixel cube. Improvements? Hierarchical algorithm does not provide adequate reduction of time required owing to sensitivity to resolution. Massive parallelization is required (and possible) for routine application of high-resolution field modeling. Subregion modeling that may be imposed by CPU requirement requires proper implementation of boundary conditions of subvolume.

Boundary and initial conditions Essential property of NLFFF models: constant ratio of current density and field strength along lines of force. Therefore: complete flux and current systems must be observed to avoid complete redirection of coronal field lines (see examples). Possible FPP implementation: observe entire active regions (and connected neighboring regions) in context with higher-frequency observations of a smaller region of interest (pre-&post- large-area scans, or SOLIS, …)

Boundary and initial conditions Including information on surrounding field For the best-fit model, the relative vector difference between input and model field has an average magnitude of 2%, and the average energy density in the field is approximated to within a few percent. Disregarding surrounding field

Chromospheric compass Photospheric field observed by FPP is not necessarily force-free. Observation of the chromospheric fibrils (using H  ) as frequently as the vector field provides a “chromospheric compass”. Observations may guide field modeling, or at least identify regions where photospheric Lorentz forces are substantial (where field model and fibril directions do not match).

Quantifying success Currently, no metric exists to quantify how well a field extrapolation matches the solar field. The absence of such a metric hinders us in setting uncertainties on estimates of (free) energy and helicity, and using the observed coronal field to guide field modeling.

3 rd NLFFF meeting A small hands-on workshop for NLFFF modelers to develop and test algorithms: June 5-7, 2006, Palo Alto, CA. For information, contact Karel Schrijver, Tom Metcalf, or Marc DeRosa.