T. Wiegelmann

How Should One Optimize Nonlinear Force-Free Coronal Magnetic Field Extrapolations from SDO/HMI Vector Magnetograms?

The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters.

Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona

We undertake a first attempt towards a consistent reconstruction of the coronal magnetic field and the coronal density structure. We consider a stationary solar corona which has to obey the equations of magnetohydrostatics. We solve these equations with help of a newly developed optimization scheme. As a first step we illustrate how tomographic information can be included into the reconstruction of coronal magnetic fields. In a second step we use coronal magnetic field information to improve the tomographic inversion process. As input the scheme requires magnetic field measurements on the photosphere from vector-magnetographs and the line-of-sight integrated density distribution from coronagraphs. We test our codes with well-known analytic magnetohydrostatic equilibria and models. The program is planned for use within the STEREO mission.

MAGNETIC ENERGY PARTITION BETWEEN THE CORONAL MASS EJECTION AND FLARE FROM AR 11283

On 2011 September 6, an X-class flare and a halo coronal mass ejection (CME) were observed from Earth erupting from the same active region AR 11283. The magnetic energy partition between them has been investigated. SDO/HMI vector magnetograms were used to obtain the coronal magnetic field using the nonlinear force-free field (NLFFF) extrapolation method. The free magnetic energies before and after the flare were calculated to estimate the released energy available to power the flare and the CME. For the flare energetics, thermal and nonthermal energies were derived using the RHESSI and GOES data. To obtain the radiative output, SDO/EVE data in the 0.1-37 nm waveband were utilized. We have reconstructed the three-dimensional (3D) periphery of the CME from the coronagraph images observed by STEREO-A, B, and SOHO. The mass calculations were then based on a more precise Thomson-scattering geometry. The subsequent estimate of the kinetic and potential energies of the CME took advantage of the more accurate mass, and the height and speed in a 3D frame. The released free magnetic energy resulting from the NLFFF model is about 6.4x10(31) erg, which has a possible upper limit of 1.8x10(32) erg. The thermal and nonthermal energies are lower than the radiative output of 2.2x10(31) erg from SDO/EVE for this event. The total radiation covering the whole solar spectrum is probably a few times larger. The sum of the kinetic and potential energy of the CME could go up to 6.5x10(31) erg. Therefore, the free energy is able to power the flare and the CME in AR 11283. Within the uncertainty, the flare and the CME may consume a similar amount of free energy.

Mesogranulation and the Solar Surface Magnetic Field Distribution

The relation of the solar surface magnetic field with mesogranular cells is studied using high spatial (≈100 km) and temporal (≈30 s) resolution data obtained with the IMaX instrument on board SUNRISE. First, mesogranular cells are identified using Lagrange tracers (corks) based on horizontal velocity fields obtained through local correlation tracking. After ≈20 minutes of integration, the tracers delineate a sharp mesogranular network with lanes of width below about 280 km. The preferential location of magnetic elements in mesogranular cells is tested quantitatively. Roughly 85% of pixels with magnetic field higher than 100 G are located in the near neighborhood of mesogranular lanes. Magnetic flux is therefore concentrated in mesogranular lanes rather than intergranular ones. Second, magnetic field extrapolations are performed to obtain field lines anchored in the observed flux elements. This analysis, therefore, is independent of the horizontal flows determined in the first part. A probability density function (PDF) is calculated for the distribution of distances between the footpoints of individual magnetic field lines. The PDF has an exponential shape at scales between 1 and 10 Mm, with a constant characteristic decay distance, indicating the absence of preferred convection scales in the mesogranular range. Our results support the view that mesogranulation is not an intrinsic convective scale (in the sense that it is not a primary energy-injection scale of solar convection), but also give quantitative confirmation that, nevertheless, the magnetic elements are preferentially found along mesogranular lanes.

MULTIWAVELENGTH OBSERVATIONS OF A PARTIALLY ERUPTIVE FILAMENT ON 2011 SEPTEMBER 8

In this paper, we report our multiwavelength observations of a partial filament eruption event in NOAA active region 11283 on 2011 September 8. A magnetic null point and the corresponding spine and separatrix surface are found in the active region. Beneath the null point, a sheared arcade supports the filament along the highly complex and fragmented polarity inversion line. After being activated, the sigmoidal filament erupted and split into two parts. The major part rose at the speeds of 90

Magnetic Loops in the Quiet Sun

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Evolution of the flaring active region NOAA 10540 as a sequence of nonlinear force-free field extrapolations

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QUASI-STATIC THREE-DIMENSIONAL MAGNETIC FIELD EVOLUTION IN SOLAR ACTIVE REGION NOAA 11166 ASSOCIATED WITH AN X1.5 FLARE

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Modeling Magnetic Field Structure of a Solar Active Region Corona using Nonlinear Force-Free Fields in Spherical Geometry

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First Use of Synoptic Vector Magnetograms for Global Nonlinear, Force-Free Coronal Magnetic Field Models

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