Abstract
Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, a modeled coronal field may be calculated from available photospheric boundary data. One class of models assumes that the corona, due to its low plasma beta, is free of Lorentz forces. Such nonlinear force-free field (NLFFF) models, when they are able to be computed, provide insight into coronal energetics without having to solve the full magneto-hydrodynamic equations, which at present are computationally infeasible at spatial resolutions needed for detailed analyses of active-region dynamics.
However, past research has established that NLFFF models are beset by problems that preclude their use on a regular basis. Some of these problems result from limitations in the data, while others are due to the models being overly idealized. In recent years, advances in modeling techniques combined with new instrumentation and data have enabled many of these issues to be addressed. Consequently, we propose to convene an International Team at ISSI to develop, test, and assess the next generation of NLFFF models to meet twice in the next two years. These models will help achieve a better understanding of the energetics and evolution of the solar corona
1. Scientific Rationale of the International Team
The dynamics of the solar corona are driven by magnetic fields. Energy release associated with the continual growth and decay of coronal magnetism leads to reconnection that in turn heats the plasma and powers solar activity, including spectacular eruptions into interplanetary space. Solar activity directly influences our
local space environment by producing violent energetic-particle storms that can damage satellite electronics, by driving ground-induced currents in electricity grids and pipelines on the surface of the Earth, and by posing radiation risks for space travelers as well as for crews on commercial aircraft using polar routes.
It is difficult to directly measure the strength and three-dimensional geometry of the coronal field. Consequently, coronal-field modeling is crucial for informing our understanding of coronal dynamics and the effects of solar activity. Such coronal-field models range from current-free extrapolations, which provide a generic impression of the large-scale geometry; to more general force-free models, which contain currents (and thus free energy) but assume the corona is in a static force-free balance; to more physically realistic, time-dependent models that capture the dynamics resulting from evolving lower-boundary inputs.
The most idealized models are current-free and are readily calculated, but they are of limited use for studying eruptive phenomena due to their inability to account for the buildup and release of free energy in active regions. At the other end of the spectrum, magnetohydrodynamic models often include prescriptions for dynamic processes such as radiative transfer and shock-wave propagation, but these models are computationally expensive and consequently can be run only for a limited selection of regions of interest and for limited durations. Between these extremes lie nonlinear force-free field (NLFFF) models, in which the low-beta coronal field is modeled as having a zero Lorentz force, but the field is still allowed to possess electric currents. This approximation is thought to provide a practical way to account for the presence of free energy in the corona without having to solve the full dynamical problem (which is much more computationally challenging).
NLFFF models require data specifying the force-free field at the boundaries of the computational domain. What is typically available, however, are vector magnetograms (giving determinations of all three components of the field) calculated from spectro-polarimetric observations of photospheric emission lines. Using these data, a typical strategy is for the numerical models to extrapolate the magnetic field upward into a coronal volume using the photospheric measurements as boundary conditions. The vector data (while not ideal, as we shall see) are widely used due to the lack of other direct measurements of magnetic fields and currents that are needed to constrain the magnetic field in the model.
From 2004 to 2009 an annual series of focused international collaborative workshops were directed at developing NLFFF modeling and applying these modeling techniques to data. At the time, NLFFF techniques were less frequently used and the limitations of the approach were not well understood. The workshops improved the basic techniques and tested them on synthetic data as well as data from the Michelson Doppler Imager (MDI; Scherrer et al. 1995) and the Solar Optical Telescope (SOT) on Hinode (Tsuneta et al. 2008). During the course of these workshops substantial progress was made, key questions and problems in the modeling process were identified, and a series of journal articles were produced (Schrijver et al. 2006; Schrijver et al. 2008; Metcalf et al. 2008; DeRosa et al. 2009). Collectively, these four articles have accumulated more 300 citations in the refereed literature since 2006.
A key finding of these earlier studies was that reconstruction of the coronal magnetic field does not consistently provide reliable estimates of important physical characteristics of active region coronae, one of which being the magnetic free energy. Contributing to this state of affairs are various factors, including:
- photospheric vector-magnetogram data are subject to (sometimes large) uncertainties, possibly arising either from the measurement process (e.g., poorly constrained spectropolarimetric inversions, signal-to-noise issues, or difficulties in resolving the 180-degree ambiguity in the resulting transverse fields) or from physical origins (e.g., variations in the line-formation height of the spectropolarimetric measurements or the non-force-free and evolving nature of the line-formation region in the photosphere);
- vector magnetogram fields of view need to be large enough to capture all relevant currents associated with an active region; and
- vector magnetograms separated by hours (the case with Hinode) are not frequent enough to allow an investigation of the energetics and evolution of, say, a flaring active region.Despite these difficulties, modeling the coronal magnetic field remains an important element in the scientific analysis of solar activity.
There is now cause for more optimism. Recently, with the advent of the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) on board the Solar Dynamics Observatory (SDO), the quality of vector-magnetograms has dramatically improved. Such data are now or will soon be available for the full solar disk every 12 minutes, with a spatial resolution of about one arc second. Correspondingly, there have been significant advances in modeling techniques since the last NLFFF workshop in 2009. These include techniques for accounting for many of the uncertainties in the photospheric field data (e.g., Wiegelmann & Inhester 2010; Petrie, Canou & Amari 2011; Valori et al. 2011; Wheatland & Leka 2011; Gilchrist, Wheatland & Leka 2012), spherical geometry (e.g., Tadesse et al. 2012), the inclusion in the models of additional observations such as coronal loop trajectories observed in ultraviolet and x-ray images (e.g., Aschwanden et al. 2012; Malanushenko et al. 2012), and the consideration of temporal variations in the data rather than the use single magnetograms (e.g., Cheung & DeRosa 2012; Sun et al. 2012).
2. Goals and Meeting Plan of the International Team
As a result of the recent improvements in both data and modeling techniques, we propose to assemble an ISSI International Team (membership listed here) to investigate, develop, and evaluate the next generation of NLFFF models. The team will collaborate in analyzing the new techniques and applying the latest codes and methods to selected time series of photospheric vector-field maps from SDO/HMI, as well as any chromospheric vector-field maps that may become available. Complementary images of the corona and chromosphere will additionally be used to constrain or verify the models. This syllabus adopts the proven approach of the past NLFFF workshops, and should further advance capabilities in coronal magnetic field modeling. The primary output of the International Team, following two 4-day meetings at ISSI held about a year apart, is a series of joint journal articles presenting new theoretical and computational techniques in modeling, together with a critical assessment of the results of their application to SDO/HMI datasets.
Prior to the first meeting, a time series of SDO/HMI vector magnetograms and associated uncertainty maps, chromospheric line-of-sight data, and coronal imagery will be prepared for use by the modelers. The modelers will then be asked to run their respective NLFFF codes on these data. At the first meeting (see agenda here), the team will:
- review the current state of modeling, including discussions of the three most widely used techniques (optimization, Grad-Rubin iteration, and magnetofrictional relaxation/evolution);
- examine, intercompare, and validate the resulting NLFFF models calculated from the previously distributed SDO/HMI dataset;
- identify problem areas with the SDO/HMI dataset that may have affected the NLFFF extrapolation process;
- assign writing tasks and co-author as a group a journal article (to be completed in the intervening year) on the SDO/HMI experiments; and
- identify an ensemble of new active regions of interest, and devise action items for the intervening year, to be completed by the time of the second meeting.
At the second meeting (see agenda here), to be held about a year after the first meeting, the International Team will:
- examine, intercompare, and validate the resulting NLFFF models calculated from the ensemble of new active-region datasets, and discuss and critically review updates to the modeling techniques;
- assign writing tasks and co-author a journal article on the second round of NLFFF experiments; and
- assess the future of NLFFF modeling.
3. Requested Facilities and Financial Support
During meetings, the International Team will require a meeting room for about 12–15 people, projection equipment, and internet connectivity. We request the standard financial support of the team members’ local expenses (lodging, meals, and incidental expenses). We request that reimbursement of the leaders’ transportation expenses be waived in favor of support for the local expenses of an extra young researcher (in addition to the standard 20% allowance), to be identified upon selection of this proposal. Publication charges of the resulting journal articles will be covered by the home institutions of the team leadership. High-performance computing facilities will be provided by the home institutions of the team members.
4. Added Value of ISSI
ISSI provides a unique meeting environment that enables collaboration amongst small groups of about a dozen participants. Having International Teams meet in a medium-sized city such as Bern is conducive to making focused progress on difficult problems, such as that of NLFFF models of the solar corona, and ISSI provides a venue equipped with fast internet and modern conferencing technology (not to mention a coffee machine) to aid in achieving the goals proposed here. Additionally, the financial support provided by ISSI aids such progress by offsetting the cost of assembling team members in a common location, who (for the team proposed here) would otherwise be dispersed across America, Europe, and Australia.
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