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Register a new userNon-linear force-free field modeling of a solar active region around the time of a major flare and coronal mass ejection
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Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and 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 pre-existing 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 Active Region 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with 4 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 ~10^32 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.
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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 article, 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 the 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.
The near-Sun kinematics of coronal mass ejections (CMEs) determine the severity and arrival time of associated geomagnetic storms. We investigate the relationship between the deprojected speed and kinetic energy of CMEs and magnetic measures of their solar sources, reconnection flux of associated eruptive events and intrinsic flux rope characteristics. Our data covers the period 2010-2014 in solar cycle 24. Using vector magnetograms of source active regions we estimate the size and nonpotentiality. We compute the total magnetic reconnection flux at the source regions of CMEs using the post-eruption arcade method. By forward modeling the CMEs we find their deprojected geometric parameters and constrain their kinematics and magnetic properties. Based on an analysis of this database we report that the correlation between CME speed and their source active region size and global nonpotentiality is weak, but not negligible. We find the near-Sun velocity and kinetic energy of CMEs to be well correlated with the associated magnetic reconnection flux. We establish a statistically significant empirical relationship between the CME speed and reconnection flux that may be utilized for prediction purposes. Furthermore, we find CME kinematics to be related with the axial magnetic field intensity and relative magnetic helicity of their intrinsic flux ropes. The amount of coronal magnetic helicity shed by CMEs is found to be well correlated with their near-Sun speeds. The kinetic energy of CMEs is well correlated with their intrinsic magnetic energy density. Our results constrain processes related to the origin and propagation of CMEs and may lead to better empirical forecasting of their arrival and geoeffectiveness.
We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other.
The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the nonpotential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of AR 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around time of major flare activity on 2011/02/15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly (HMI and AIA, respectively) onboard the Solar Dynamics Observatory (SDO). The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input, and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring, and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about $1times10^{32}$ erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by $approx0.9$ full turns about its axis.
In this article, we investigate the formation and disruption of a coronal sigmoid from the active region (AR) NOAA 11909 on 07 December 2013, by analyzing multi-wavelength and multi-instrument observations. Our analysis suggests that the formation of `transient sigmoid initiated $approx$1 hour before its eruption through a coupling between two twisted coronal loop systems. A comparison between coronal and photospheric images suggests that the coronal sigmoid was formed over a simple $beta$-type AR which also possessed dispersed magnetic field structure in the photosphere. The line-of-sight photospheric magnetograms also reveal moving magnetic features, small-scale flux cancellation events near the PIL, and overall flux cancellation during the extended pre-eruption phase which suggest the role of tether-cutting reconnection toward the build-up of the flux rope. The disruption of the sigmoid proceeded with a two-ribbon eruptive M1.2 flare (SOL2013-12-07T07:29). In radio frequencies, we observe type III and type II bursts in meter wavelengths during the impulsive phase of the flare. The successful eruption of the flux rope leads to a fast coronal mass ejection (with a linear speed of $approx$1085 km s -1 ) in SOHO/LASCO field-of-view. During the evolution of the flare, we clearly observe typical sigmoid-to-arcade transformation. Prior to the onset of the impulsive phase of the flare, flux rope undergoes a slow rise ($approx$15 km s -1 ) which subsequently transitions into a fast eruption ($approx$110 km s -1 ). The two-phase evolution of the flux rope shows temporal associations with the soft X-ray precursor and impulsive phase emissions of the M-class flare, respectively, thus pointing toward a feedback relationship between magnetic reconnection and early CME dynamics.
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