Tahar Amari

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.

Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. II. Turbulent Diffusion-driven Evolution

We consider a three-dimensional bipolar magnetic field B, occupying a half-space, which is driven into evolution by the slow turbulent diffusion of its normal component on the boundary. The latter is imposed by fixing the tangential component of the electric field and leads to flux cancellation. We first present general analytical considerations on this problem and then construct a class of explicit solutions in which B keeps evolving quasi-statically through a sequence of force-free configurations without exhibiting any catastrophic behavior. Thus, we report the results of a series of numerical simulations in which B evolves from different force-free states, the electric field on the boundary being imposed to have a vanishing electrostatic part (the latter condition is not enforced in the analytical model, and thus it is possible a priori for the results of the two types of calculations to be different). In all the cases, we find that the evolution conserves the magnetic helicity and exhibits two qualitatively different phases. The first one, during which a twisted flux rope is created, is slow and almost quasi-static, while the second one is associated with a disruption, which is confined for a small initial helicity and global for a large initial helicity. Our calculations may be relevant for modeling the coronal mass ejections that have been observed to occur in the late dispersion phase of an active region. In particular, they may allow us to understand the role played by a twisted flux rope in these events.

Flux cancellation and coronal mass ejections

Time dependent magnetohydrodynamic computations of the flux cancellation mechanism are presented. Previous authors have discussed this mechanism as a possible cause for the formation of prominences and the trigger for prominence eruptions and coronal mass ejections (CMEs). This paper shows that flux cancellation in an energized two-and-one-half-dimensional helmet streamer configuration first leads to the formation of stable flux rope structures. When a critical threshold of flux reduction is exceeded, the configuration erupts violently. Significant amounts of stored magnetic energy are released through magnetic reconnection. The ejected flux rope propagates out into the solar wind and forms an interplanetary shock wave. A similar eruption occurs for a three-dimensional calculation where the ends of the flux rope field lines are anchored to the Sun. The flux cancellation mechanism unifies the processes of prominence formation, prominence eruption, and CME initiation, and thus provides an attractive hypothesis for explaining the cause of these dynamic events.Time dependent magnetohydrodynamic computations of the flux cancellation mechanism are presented. Previous authors have discussed this mechanism as a possible cause for the formation of prominences and the trigger for prominence eruptions and coronal mass ejections (CMEs). This paper shows that flux cancellation in an energized two-and-one-half-dimensional helmet streamer configuration first leads to the formation of stable flux rope structures. When a critical threshold of flux reduction is exceeded, the configuration erupts violently. Significant amounts of stored magnetic energy are released through magnetic reconnection. The ejected flux rope propagates out into the solar wind and forms an interplanetary shock wave. A similar eruption occurs for a three-dimensional calculation where the ends of the flux rope field lines are anchored to the Sun. The flux cancellation mechanism unifies the processes of prominence formation, prominence eruption, and CME initiation, and thus provides an attractive hypothe...

Well posed reconstruction of the solar coronal magnetic field

We present and compare two methods for the reconstruction of the solar coronal magnetic field, assumed to be force-free, from photospheric boundary data. Both methods rely on a well posed mathematical boundary value problem and are of the Grad-Rubin type, i.e., the couple

3D Coronal magnetic field from vector magnetograms: non-constant-

({vec B},alpha)

\alpha

is computed iteratively. They do differ from each other on the one hand by the way they address the zero-divergence ofxa0

force-free configuration of the active region NOAA 8151

{vec B}

A TWISTED FLUX ROPE AS THE MAGNETIC STRUCTURE OF A FILAMENT IN ACTIVE REGION 10953 OBSERVED BY HINODE

xa0issue, and on the other hand by the scheme they use for computingxa0 α at each iteration. The comparison of the two methods is done by numerically computing two examples of nonlinear force-free fields associated to large scale strong electric current distributions, whose exact forms can be otherwise determined semi-analytically. In particular, the second solution has a large nonlinearity even in the weak field region – a feature which is not present in the actual magnetograms, but is interesting to consider as it does allow to push the methods to the limits of their range of validity. The best results obtained with those methods give a relative vector error smaller thanxa00.01. For the latter extreme case, our results show that higher resolution reconstructions with bounded convergence improve the approximated solution, which may be of some interest for the treatment of the data of future magnetographs.

Magnetic Field Topology in Prominences

The Active Region 8151 (AR 8151) observed in February 1998 is the site of an eruptive event associated with a fila- ment and a S-shaped structure, and producing a slow Coronal Mass Ejection (CME). In order to determine how the CME occurs, we compute the 3D coronal magnetic field and we derive some relevant parameters such as the free magnetic energy and the relative magnetic helicity. The 3D magnetic configuration is reconstructed from photospheric magnetic magnetograms (IVM, Mees Solar Observatory) in the case of a non-constant- force-free (nl) field model. The reconstruction method is divided into three main steps: the analysis of vector magnetograms (transverse fields, vertical density of electric current, ambiguity of 180), the numerical scheme for the nl magnetic field, the interpretation of the computed magnetic field with respect to the observations. For AR 8151, the nl field matches the coronal observations from EIT/SOHO and from SXT/Yohkoh. In particu- lar, three characteristic flux tubes are shown: a highly twisted flux tube, a long twisted flux tube and a quasi-potential flux tube. The maximum energy budget is estimated to 2:6 10 31 erg and the relative magnetic helicity to 4:7 10 34 G 2 cm 4 .F rom the simple photospheric magnetic distribution and the evidence of highly twisted flux tubes, we argue that the flux rope model is the most likely to describe the initiation mechanism of the eruptive event associated with AR 8151.