Stephane Regnier

A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953

Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

Nonlinear Force‐free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection

Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.

Evolution of magnetic fields and energetics of flares in active region 8210

To better understand eruptive events in the solar corona, we combine sequences of multi-wavelength observations and modelling of the coronal magnetic field of NOAA AR 8210, a highly flare-productive active region. From the photosphere to the corona, the observations give us information about the motion of magnetic elements (photospheric magnetograms), the location of flares (e.g., Hα, EUV or soft X-ray brightenings), and the type of events (Hα blueshift events). Assuming that the evolution of the coronal magnetic field above an active region can be described by successive equilibria, we follow in time the magnetic changes of the 3D nonlinear force-free (nlff) fields reconstructed from a time series of photospheric vector magnetograms. We apply this method to AR 8210 observed on May 1, 1998 between 17:00 UT and 21:40 UT. We identify two types of horizontal photospheric motions that can drive an eruption: a clockwise rotation of the sunspot, and a fast motion of an emerging polarity. The reconstructed nlff coronal fields give us a scenario of the confined flares observed in AR 8210: the slow sunspot rotation enables the occurence of flare by a reconnection process close to a separatrix surface whereas the fast motion is associated with small-scale reconnections but no detectable flaring activity. We also study the injection rates of magnetic energy, Poynting flux and relative magnetic helicity through the photosphere and into the corona. The injection of magnetic energy by transverse photospheric motions is found to be correlated with the storage of energy in the corona and then the release by flaring activity. The magnetic helicity derived from the magnetic field and the vector potential of the nlff configuration is computed in the coronal volume. The magnetic helicity evolution shows that AR 8210 is dominated by the mutual helicity between the closed and potential fields and not by the self helicity of the closed field which characterizes the twist of confined flux bundles. We conclude that for AR 8210 the complex topology is a more important factor than the twist in the eruption process.

3D magnetic configuration of the Halpha filament and X-ray sigmoid in NOAA AR 8151

We investigate the structure and relationship of an Hα filament and an X-ray sigmoid observed in active region NOAA 8151. We first examine the presence of such structures in the reconstructed 3D coronal magnetic field obtained from the non-constant-α force-free field hypothesis using a photospheric vector magnetogram (IVM, Mees Solar Observatory). This method allows us to identify several flux systems: a filament (height 30 Mm, aligned with the polarity inversion line (PIL), magnetic field strength at the apex 49 G, number of turns 0.5-0.6), a sigmoid (height 45 Mm, aligned with the PIL, magnetic field strength at the apex 56 G, number of turns 0.5-0.6) and a highly twisted flux tube (height 60 Mm, magnetic field strength at the apex 36 G, number of turns 1.1-1.2). By searching for magnetic dips in the configuration, we identify a filament structure which is in good agreement with the Hα observations. We find that both filament and sigmoidal structures can be described by a long twisted flux tube with a number of turns less than 1 which means that these structures are stable against kinking. The filament and the sigmoid have similar absolute values of α and Jz in the photosphere. However, the electric current density is positive in the filament and negative in the sigmoid: the filament is right-handed whereas the sigmoid is left-handed. This fact can explain the discrepancies between the handedness of magnetic clouds (twisted flux tubes ejected from the Sun) and the handedness of their solar progenitors (twisted flux bundles in the low corona). The mechanism of eruption in AR 8151 is more likely not related to the development of instability in the filament and/or the sigmoid but is associated with the existence of the highly twisted flux tube (∼1.1-1.2 turns).

A new view of quiet-Sun topology from Hinode/SOT

Context. With the recent launch of the Hinode satellite our view of the nature and evolution of quiet-Sun regions has been improved. In light of the new high resolution observations, we revisit the study of the quiet Sun’s topological nature. Aims. Topology is a tool to explain the complexity of the magnetic field, the occurrence of reconnection processes, and the heating of the corona. This Letter aims to give new insights to these different topics. Methods. Using a high-resolution Hinode/SOT observation of the line-of-sight magnetic field on the photosphere, we calculate the three dimensional magnetic field in the region above assuming a potential field. From the 3D field, we determine the existence of null points in the magnetic configuration. Results. From this model of a continuous field, we find that the distribution of null points with height is significantly different from that reported in previous studies. In particular, the null points are mainly located above the bottom boundary layer in the photosphere (54%) and in the chromosphere (44%) with only a few null points in the corona (2%). The density of null points (expressed as the ratio of the number of null points to the number of photospheric magnetic fragments) in the solar atmosphere is estimated to be between 3% and 8% depending on the method used to identify the number of magnetic fragments in the observed photosphere. Conclusions. This study reveals that the heating of the corona by magnetic reconnection at coronal null points is unlikely. Our findings do not rule out the heating of the corona at other topological features. We also report the topological complexity of the chromosphere as strongly suggested by recent observations from Hinode/SOT.

Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State

To understand the physics of solar flares, including the local reorganization of the magnetic field and the acceleration of energetic particles, we have first to estimate the free magnetic energy available for such phenomena, which can be converted into kinetic and thermal energy. The free magnetic energy is the excess energy of a magnetic configuration compared to the minimum-energy state, which is a linear force-free field if the magnetic helicity of the configuration is conserved. We investigate the values of the free magnetic energy estimated from either the excess energy in extrapolated fields or the magnetic virial theorem. For four different active regions, we have reconstructed the nonlinear force-free field and the linear force-free field corresponding to the minimum-energy state. The free magnetic energies are then computed. From the energy budget and the observed magnetic activity in the active region, we conclude that the free energy above the minimum-energy state gives a better estimate and more insights into the flare process than the free energy above the potential field state.

A new look at a polar crown cavity as observed by SDO/AIA Structure and dynamics

Context. The Solar Dynamics Observatory (SDO) was launched in February 2010 and is now providing an unprecedented view of the solar activity at high spatial resolution and high cadence covering a broad range of temperature layers of the atmosphere. Aims. We aim at defining the structure of a polar crown cavity and describing its evolution during the erupting process. Methods. We use the high-cadence time series of SDO/AIA observations at 304 A (50 000 K) and 171 A (0.6 MK) to determine the structure of the polar crown cavity and its associated plasma, as well as the evolution of the cavity during the different phases of the eruption. We report on the observations recorded on 13 June 2010 located on the north-west limb. Results. We observe coronal plasma shaped by magnetic field lines with a negative curvature (U-shape) sitting at the bottom of a cavity. The cavity is located just above the polar crown filament material. We thus observe the inner part of the cavity above the filament as depicted in the classical three part coronal mass ejection (CME) model composed of a filament, a cavity, and a CME front. The filament (in this case a polar crown filament) is part of the cavity, and it makes a continuous structuring from the filament to the CME front depicted by concentric ellipses (in a 2D cartoon). Conclusions. We propose to define a polar crown cavity as a density depletion sitting above denser polar crown filament plasma drained down the cavity by gravity. As part of the polar crown filament, plasma at different temperatures (ranging from 50 000 K to 0.6 MK) is observed at the same location on the cavity dips and sustained by a competition between the gravity and the curvature of magnetic field lines. The eruption of the polar crown cavity as a solid body can be decomposed into two phases: a slow rise at a speed of 0.6 km s −1 and an acceleration phase at a mean speed of 25 km s −1 .

Nonlinear force-free models for the solar corona I. Two active regions with very different structure

Context. With the development of new instrumentation providing measurements of solar photospheric vector magnetic fields, we need to develop our understanding of the effects of current density on coronal magnetic field configurations. Aims. The object is to understand the diverse and complex nature of coronal magnetic fields in active regions using a nonlinear forcefree model. Methods. From the observed photospheric magnetic field we derive the photospheric current density for two active regions: one is a decaying active region with strong currents (AR8151), and the other is a newly emerged active region with weak currents (AR8210). We compare the three-dimensional structure of the magnetic fields for both active region when they are assumed to be either potential or nonlinear force-free. The latter is computed using a Grad-Rubin vector-potential-like numerical scheme. A quantitative comparison is performed in terms of the geometry, the connectivity of field lines, the magnetic energy and the magnetic helicity content. Results. For the old decaying active region the connectivity and geometry of the nonlinear force-free model include strong twist and strong shear and are very different from the potential model. The twisted flux bundles store magnetic energy and magnetic helicity high in the corona (about 50 Mm). The newly emerged active region has a complex topology and the departure from a potential field is small, but the excess magnetic energy is stored in the low corona and is enough to trigger powerful flares.

A self-consistent nonlinear force-free solution for a solar active region magnetic field

Nonlinear force-free solutions for the magnetic field in the solar corona constructed using photospheric vector magnetic field boundary data suffer from a basic problem: the observed boundary data are inconsistent with the nonlinear force-free model. Specifically, there are two possible choices of boundary conditions on vertical current provided by the data, and the two choices lead to different force-free solutions. A novel solution to this problem is described. Bayesian probability is used to modify the boundary values on current density, using field-line connectivity information from the two force-free solutions and taking into account uncertainties, so that the boundary data are more consistent with the two nonlinear force-free solutions. This procedure may be iterated until a set of self-consistent boundary data (the solutions for the two choices of boundary conditions are the same) is achieved. The approach is demonstrated to work in application to Hinode/Solar Optical Telescope observations of NOAA active region 10953.

The influence of spatial resolution on nonlinear force-free modeling

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.