THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING

Data-driven modelling of solar coronal magnetic field evolution and eruptions

Magnetic fields play a fundamental role in the structure and dynamics of the solar corona. As they are driven by their footpoint motions on the solar surface, which transport energy from the interior of the Sun into its atmosphere, the coronal magnetic fields are stressed continuously with buildup of magnetic nonpotentiality in the form of topology complexity (magnetic helicity) and local electric currents (magnetic free energy). The accumulated nonpotentiality is often released explosively by solar eruptions, manifested as solar flares and coronal mass ejections, during which magnetic energy is converted into mainly kinetic, thermal, and nonthermal energy of the plasma, which can cause adverse space weather. To reveal the physical mechanisms underlying solar eruptions, it is vital to know the three-dimensional (3D) structure and evolution of the coronal magnetic fields. Because of a lack of direct measurements, the 3D coronal magnetic fields are commonly studied using numerical modeling, whereas traditional models mostly aim for a static extrapolation of the coronal field from the observable photospheric magnetic field data. Over the last decade, dynamic models that are driven directly by observation magnetograms have been developed and applied successfully to study solar coronal magnetic field evolution as well as its eruption, which offers a novel avenue for understanding their underlying magnetic topology and mechanism. In this paper, we review the basic methodology of the data-driven coronal models, state-of-the-art developments, their typical applications, and new physics that have been derived using these models. Finally, we provide an outlook for future developments and applications of the data-driven models.

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Data-driven models offer a novel avenue to study solar coronal magnetic fields

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Such numerical models are directly driven by continuously-observed magnetograms

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They are able to reproduce the magnetic structures and evolutions of solar eruptions

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They help shed new light on the physical mechanisms of complex solar eruptions

Flare-productive active regions

Strong solar flares and coronal mass ejections, here defined not only as the bursts of electromagnetic radiation but as the entire process in which magnetic energy is released through magnetic reconnection and plasma instability, emanate from active regions (ARs) in which high magnetic non-potentiality resides in a wide variety of forms. This review focuses on the formation and evolution of flare-productive ARs from both observational and theoretical points of view. Starting from a general introduction of the genesis of ARs and solar flares, we give an overview of the key observational features during the long-term evolution in the pre-flare state, the rapid changes in the magnetic field associated with the flare occurrence, and the physical mechanisms behind these phenomena. Our picture of flare-productive ARs is summarized as follows: subject to the turbulent convection, the rising magnetic flux in the interior deforms into a complex structure and gains high non-potentiality; as the flux appears on the surface, an AR with large free magnetic energy and helicity is built, which is represented by δ -sunspots, sheared polarity inversion lines, magnetic flux ropes, etc; the flare occurs when sufficient magnetic energy has accumulated, and the drastic coronal evolution affects magnetic fields even in the photosphere. We show that the improvement of observational instruments and modeling capabilities has significantly advanced our understanding in the last decades. Finally, we discuss the outstanding issues and future perspective and further broaden our scope to the possible applications of our knowledge to space-weather forecasting, extreme events in history, and corresponding stellar activities.

Time-dependent Data-driven Modeling of Active Region Evolution Using Energy-optimized Photospheric Electric Fields

In this work, we present results of a time-dependent data-driven numerical simulation developed to study the dynamics of coronal active region magnetic fields. The evolving boundary condition driving the model, the photospheric electric field, is inverted using a time sequence of vector magnetograms as input. We invert three distinct electric field datasets for a single active region. All three electric fields reproduce the observed evolution of the normal component of the magnetic field. Two of the datasets are constructed so as to match the energy input into the corona to that provided by a reference estimate. Using the three inversions as input to a time-dependent magnetofrictional model, we study the response of the coronal magnetic field to the driving electric fields. The simulations reveal the magnetic field evolution to be sensitive to the input electric field despite the normal component of the magnetic field evolving identically and the total energy injection being largely similar. Thus, we demonstrate that the total energy injection is not sufficient to characterize the evolution of the coronal magnetic field: coronal evolution can be very different despite similar energy injections. We find the relative helicity to be an important additional metric that allows one to distinguish the simulations. In particular, the simulation with the highest relative helicity content produces a coronal flux rope that subsequently erupts, largely in agreement with extreme-ultraviolet imaging observations of the corresponding event. Our results suggest that time-dependent data-driven simulations that employ carefully constructed driving boundary conditions offer a valuable tool for modeling and characterizing the evolution of coronal magnetic fields.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (10.1007/s11207-019-1430-x) contains supplementary material, which is available to authorized users.

Assessing the Quality of Models of the Ambient Solar Wind

In this paper we present an assessment of the status of models of the global Solar Wind in the inner heliosphere. We limit our discussion to the class of models designed to provide solar wind forecasts, excluding those designed for the purpose of testing physical processes in idealized configurations. In addition, we limit our discussion to modeling of the 'ambient' wind in the absence of coronal mass ejections. In this assessment we cover use of the models both in forecast mode and as tools for scientific research. We present a brief history of the development of these models, discussing the range of physical approximations in use. We discuss the limitations of the data inputs available to these models and its impact on their quality. We also discuss current model development trends.

Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse

Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models.

On Flare-CME Characteristics from Sun to Earth Combining Remote-Sensing Image Data with In Situ Measurements Supported by Modeling

We analyze the well-observed flare and coronal mass ejection (CME) from 1 October 2011 (SOL2011-10-01T09:18) covering the complete chain of effects - from Sun to Earth - to better understand the dynamic evolution of the CME and its embedded magnetic field. We study in detail the solar surface and atmosphere associated with the flare and CME using the Solar Dynamics Observatory (SDO) and ground-based instruments. We also track the CME signature off-limb with combined extreme ultraviolet (EUV) and white-light data from the Solar Terrestrial Relations Observatory (STEREO). By applying the graduated cylindrical shell (GCS) reconstruction method and total mass to stereoscopic STEREO-SOHO (Solar and Heliospheric Observatory) coronagraph data, we track the temporal and spatial evolution of the CME in the interplanetary space and derive its geometry and 3D mass. We combine the GCS and Lundquist model results to derive the axial flux and helicity of the magnetic cloud (MC) from in situ measurements from Wind. This is compared to nonlinear force-free (NLFF) model results, as well as to the reconnected magnetic flux derived from the flare ribbons (flare reconnection flux) and the magnetic flux encompassed by the associated dimming (dimming flux). We find that magnetic reconnection processes were already ongoing before the start of the impulsive flare phase, adding magnetic flux to the flux rope before its final eruption. The dimming flux increases by more than 25% after the end of the flare, indicating that magnetic flux is still added to the flux rope after eruption. Hence, the derived flare reconnection flux is most probably a lower limit for estimating the magnetic flux within the flux rope. We find that the magnetic helicity and axial magnetic flux are lower in the interplanetary space by ∼ 50% and 75%, respectively, possibly indicating an erosion process. A CME mass increase of 10% is observed over a range of [Formula: see text]. The temporal evolution of the CME-associated core-dimming regions supports the scenario that fast outflows might supply additional mass to the rear part of the CME.

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin (Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.