ISSI Team Proposal

Data-driven 3D Modeling of Evolving and Eruptive Solar Active Region Coronae

Proposed by

Georgios Chintzoglou

Lockheed Martin Solar & Astrophysics Laboratory 3176 Porter Dr (Bldg 252), Palo Alto, CA 94304, USA

and

Michael S. Wheatland

Sydney Institute for Astronomy, School of Physics The University of Sydney, Sydney, NSW 2006, Australia

Abstract

Over the last decades we have seen great progress in our understanding of the genesis of solar active regions (ARs) thanks to advanced 3D radiative-convective MHD simulations. These models are initialized with lower boundary conditions or, e.g., magnetic field concentrations below the photosphere, and can simulate the formation of sunspots all the way to the formation of fully-developed ARs and even successfully produce eruptive flares in the simulated corona. However, such methods are extremely computationally-expensive and require additional knowledge of the sub-photospheric magnetic field configuration, that is typically not available from observations. Thus, such models can only be employed a posteriori, i.e., once an AR has been already observed to emerge and develop, from which one may gain insight into what was the sub-photospheric magnetic configuration that drove the magnetic evolution at the surface and the activity observed. Such advanced 3D models are thus termed “data-inspired”, as in “inspired from observations”, but they are not able to simulate a specific event.

A separate class of 3D models has been developed to complement these advanced “data-inspired” MHD models. Such models rely on simplifications, e.g., assuming the absence of plasma in the corona and that the magnetic field there is “force-free” (i.e., electric currents are aligned with the magnetic field). These models are produced as the solution to a boundary value problem, with the bottom boundary being a single photospheric magnetic field map that is readily available from the observations. This class of models, known as “data-constrained”, is widely used by the community, despite the strong physical assumptions that are obviously incorrect. In addition, such models are only able to provide static solutions, and therefore are unable to capture the dynamic aspects of the evolving magnetic field in the AR corona. To properly account for the time-evolution in AR fields, a model should be able to retain a “memory” of the previous state of the field in the corona while the photosphere (bottom boundary) is evolving, e.g., due to the emergence and development of an AR. Such advantage is offered by a class of 3D models known as “data-driven”. These models are capable at simulating specific events, and they are based on the data available from observations. Hence they have advantages over both the “data-inspired” and “data-constrained” approches. Thus, “data-driven” models appear to be a highly promising tool for understanding the dynamics of AR coronae. Several “data-driven” models have been developed by different teams around the world. However, different models use different methods for boundary-driving and/or make different assumptions for the coronal environment, e.g., whether it is plasma-free (nonlinear force-free magnetofrictional modeling) or not (e.g., “data-driven” 3D MHD).

We therefore propose to convene an International Team at ISSI to bring together world experts in solar observations and solar AR modeling. The goal of the Team will be to develop, test, and quantitatively assess the next generation of “data-driven” models. The Team will meet twice in the next two years. The results of this collaboration will improve our understanding of the energetics and evolution of the solar corona, bringing our field closer to the ultimate goal of accurate flare and CME prediction.

1. Scientific Rationale

Magnetic fields govern all aspects of solar activity, from the 11-year solar cycle to the most energetic events in the solar system, namely solar flares and Coronal Mass Ejections (CMEs), which threaten our modern technological civilization. As seen on the surface of the Sun, this activity emanates from localized concentrations of magnetic fields, which emerge sporadically from the solar interior. These locations are called solar Active Regions (ARs). During the period from AR birth to matu- rity, and depending on their magnetic complexity as seen at the surface (i.e., bipolar or of mixed polarity/multipolar), a varying degree of flaring and explosive activity may be observed due to rapid magnetic energy release by magnetic reconnection in the corona. In addition, as the ARs decay and their magnetic configuration simplifies, it is also possible for them to produce CME eruptions. How- ever, progress in understanding the exact physical processes behind AR explosive activity is inhibited by our present inability to measure the full 3D vector of the magnetic field in the solar corona volume. What is certain is that the energy stored in the AR coronal field must be above that of the potential field in order to have the free energy required to produce eruptions and flares. Different scenarios have been explored with “data-inspired” models, i.e., numerical simulations which aim to reproduce the flare and CME phenomenology in idealized numerical setups with various degrees of realism (for a state-of-the-art in terms of realism, see Cheung et al. 2019). However, such modeling efforts cannot simulate the evolution of an actual AR or specific events as these require prior knowledge of the AR’s 3D subphotospheric magnetic configuration, which is also, at present, not possible.

Because direct observations of the 3D coronal field at high resolution are not currently feasible, our attempts to explain coronal activity have to rely on idealized and oversimplified models of the solar corona. In contrast, vector magnetic fields at the photosphere can be measured in high time-cadence and spatial resolution in the form of “magnetogram maps”, covering the entire solar disk, thus providing the “bottom boundary” for the “visible parts” of solar ARs. This has enabled us to compensate for our lack of information on the 3D coronal field with the development of idealized 3D “data-constrained” models. This is done by neglecting the presence of coronal plasma paired with the assumption of a nonlinear force-free (NLFF) field for the corona and by solving the 3D boundary value problem with the observed photospheric vector field maps as the bottom boundary condition. This approximation provides a practical way to estimate the free energy in the corona by avoiding the solution of the full set of the MHD equations. Such 3D NLFF models can be further split into two categories based on how they achieve the solution, i.e., (i) optimization models reaching the equillibrium via iterative optimization schemes minimizing a penalty function (e.g., Wheatland et al. 2000; Wiegelmann et al. 2012); and (ii) Magnetofrictional (MF) relaxation models which iteratively “evolve” the magnetic induction equation using a velocity field that advances the solution to a more force-free state (Chodura & Schlueter 1981; Roumeliotis 1996; Valori et al. 2012b). However, because the “data-constrained” NLFF models are – by design – static models, they are assumed to represent static NLFF equillibria for the 3D boundary value problems they solve.

Such “data-constrained” models have been used extensively by the community in recovering evidence for pre-eruptive magnetic structures (such as magnetic flux ropes; MFRs) and for inferring the non- potential energy build-up-and-release before and after eruptions (e.g., Amari et al. 2014). Yet, recent works suggest that the long-term evolution of magnetic fields may play a primary role in ARs devel- oping unstable pre-eruptive structures (MFRs), not only for decaying ARs (e.g., formation of filament channels; MacKay 2015), but also for emerging ARs (e.g., Chintzoglou et al. 2019). Such evolutionary aspects are neglected in static “data-constrained” NLFF models. Therefore, the next generation of models for the AR coronae should capture the evolutionary history of the underlying magnetic fields. It is generally recognized that there is great potential in approaches to modeling which capture the temporal variations in the data, instead of “data-constrained” reconstructions based on individual magnetograms (e.g., Cheung & DeRosa 2012; Jiang et al. 2016; Yeates 2017; Yardley et al. 2018; Pomoell et al. 2019; Price et al. 2019; Chintzoglou et al. 2019). Such models are called “data-driven”, to emphasize that key difference in comparison to “data-constrained” models. However, these models, developed by different teams around the world, use different techniques to drive the model corona to an energized state compatible with observations at the photosphere. This includes driving the boundary directly with the magnetogram data, or by an estimation of electric fields, the derivation of which may depend on different models or assumptions, e.g., optical flow-tracking techniques, such as DAVE4VM (Schuck et al. 2005), or the PDFI method which also includes Doppler measurements (Kazachenko et al. 2014; Fisher et al. 2015; Chintzoglou et al. 2019). Note that initial tests (Toriumi et al. 2020) report better performance for codes with electric field driving.

Traditionally, attempts to understand what causes a flare/CME in an AR only focus on specific events. The vast majority of such case studies employ “data-constrained” NLFF extrapolations, e.g., before and after the event(s), or a series of static models at regular intervals spanning the time period around the flare. Recent studies on a large number of eruptive ARs (e.g., Duan et al. 2019) confirm previous evidence that MFRs are often found in such models before the time of eruption. However, to what extent the modeled 3D pre-eruptive structures and the energies from a “data-driven” code differ from those from “data-constrained” MF-relaxation or optimization NLFF models is not clear. Quantitative intercomparison between “data–constrained” and “data-driven” models is therefore necessary.

Indications for eruptions of pre-eruptive structures have been found in “data-driven” models in close association with the timeline of observed eruptive events (e.g., Fisher et al. 2015, Yardley et al. 2018, Chintzoglou et al. 2019). However, each of the existing “data-driven” codes treats boundary conditions and model-driving in different ways and these different methods have not been tested using the same boundary conditions/time-series of vector magnetograms. It is therefore timely to assess the relative strengths and weaknesses of different “data-driven” methods, and to compare the performance of these models to the corresponding “data-constrained” methods in a systematic way. The constructive exchange of knowledge and the contrasting of different modeling philosophies is inevitably mutually beneficial. Indeed, “data-driven” MF models seem promising with a good balance between (a) computational expense and (b) proper representation of the time-dependent physics (Table 1). On the other hand, another approach, known as “data-driven MHD”, has been developed for additional realism and synthesis of observables enabling direct comparisons with the observations (such as EUV images or spectral/polarimetric data), although such models are significantly more computationally-expensive.

In the near future, DKIST will begin to provide unique multi-layer magnetogram observations and we expect that such unique datasets will require time-evolving models for interpretation (e.g., de- veloped from long SDO/HMI time-series for the large-scale structures, but also resolving smaller scale-sizes/time-scales for application to the much-higher-resolution DKIST data). In addition, novel observations with Solar Orbiter will 1. expand solar surface surveillance and provide data quasi- corotating with the Sun, effectively producing longer time-series of AR evolution; and 2. will provide us with multi-viewpoint observations of stressed AR magnetic structures (in EUV), which will require robust 3D modeling for their interpretation, both of which will require the use of robust and reliable “data-driven” models. Establishing the credibility of advanced model reconstructions over previous methods will propel the field in ways not possible with standard approaches. The time to act is now.

2. Goals and Meeting Plan of the International Team

Note: The Team now includes the following additional members: Dr. Andrei Afanasef, Dr. Mark Cheung, Dr. Marc DeRosa, Prof. Duncan Mackay, Dr. Benoit Tremblay, and Dr. Thomas Wiegelmann.

Considering 1. the recent improvements in the available magnetogram data (i.e., a full-solar-cycle worth of high-resolution full-disk vector magnetograms at a 720 s and also at 120 s-cadence with the SDO/HMI; Scherrer et al. 2012); 2. the corresponding EUV imaging amassed (SDO/AIA; Lemen et al. 2012); and 3. the aforementioned diversity of modeling approaches currently in use, we propose to convene an International Team at ISSI to develop, test, and assess the performance of the next generation of advanced evolutionary 3D models of AR coronae. This multidisciplinary and diverse ISSI Team (with members from 7 different countries; Table 2) will bring together experts in solar observations (AR evolution and activity, analysis of EUV observations, spectropolarimetric inversions, disambiguation of magnetograms) and experts in all relevant aspects of solar AR modeling (“data- constrained” NLFF/MF, “data-driven” MF and even expertise in “data-inspired” modeling due to the technical origin of “data-driven” 3D MHD codes). The Team will apply the different models and techniques to (a) photospheric (and chromospheric) vector magnetogram time-series produced from a publicly available “data-inspired” 3D MHD simulation of a solar eruption (Cheung et al. 2019) and (b) time-series of SDO/HMI vector magnetograms and other associated maps (e.g., including uncertainties, different disambiguation quality, etc) for a choice of well-observed ARs (e.g., transiting at latitudes close to disk center) emerging or decaying with or without eruptive activity (Table 3).

• discuss the current state of the art in modeling AR coronae with different methods (i.e., “data- constrained” Optimization/MF and “data-driven” MF/MHD) and quantitative comparisons.
• assess how methods perform on the noise-free and artificially-noisy synthetic phot./chrom. vector magnetogram series from the publicly available 3D radiative MHD simulation of a solar eruption.
• analyze models produced from the provided observational HMI time-series (Table 3) and validate results against observations via synthesis of observables (“data-driven” MHD) or proxies (“data-constrained” Optimization/MF or “data-driven” MF) (see Table 1).
• identify a new set of four ARs (e.g., from Cycle 25, possibly expanded with DKIST/Solar Orbiter data) to be modeled with all methods, which will be used for testing over the following year.
• assign preliminary writing tasks to Team members for journal article(s).

At the second meeting (a year later) the Team will:

• juxtapose and cross-validate results between different methods and the observations; if the ob- served phenomenology is replicated satisfactorily (e.g., onset of eruptions were successfully re- produced in any of the models), discuss the physics scenarios produced by the models, which govern the evolution of the observed ARs.
• assess the current state of the art and a pathway to the future of “data-driven” modeling, with an emphasis on new instrumentation required to further improve the data products and improve capabilities for prediction (e.g., need for a new generation of high-resolution and high-sensitivity photospheric/chromospheric magnetographs? L5 Mission?)
• perform final assessment of the overall maturity of the project and its results from last year, and finalize the writing tasks for journal article(s).

3. Requested Facilities and Financial Support

The high performance computing needed for the execution of the various modeling tasks will be provided by the home institutions of the Team members. To facilitate our collaboration we request a large meeting room (≈16 people including the young scientists; TBD) with a video projector, white-boards and fast internet access. Standard ISSI support covering the living and accommodation expenses of the Team members is also requested. Publication costs for the planned product outputs would also be covered by the home institutes of the Team’s leaders.

4. Added Value of ISSI

The results from the exhaustive comparison between these advanced 3D models will improve our understanding of the energetics and evolution of solar AR coronae, bringing our field closer to the ultimate goal of accurate flare and CME prediction. ISSI adds value by facilitating this synergy to develop fruitfully by providing an environment which enables the exchange of scientific ideas between a small team of experts. Importantly, ISSI provides financial support which will allow this diverse Team from 7 countries and 4 continents to assemble.

(Edit: List of references provided in a separate tab in this webpage)