A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram

Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free.     

Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124

Solar eruptive phenomena, like flares and coronal mass ejections (CMEs), are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field to only the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using nonlinear force-free field (NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three-dimensional magnetic field, we calculate the three-dimensional electric current density and magnetic energy throughout the solar atmosphere for Carrington rotation 2124 using our global extrapolation code. We found that spatially, the low-lying, current-carrying core field demonstrates a strong concentration of free energy in the active-region core, from the photosphere to the lower corona (about 70 Mm). The free energy density appears largely co-spatial with the electric current distribution.     

The Evolution of Quasi-Separatrix Layer in Two Solar Eruptive Events

Quasi-separatrix layer, also called as QSL, is a region where magnetic connectivity changes drastically, and mostly well coincides with the location of flare ribbons in observations. The research on the relations of this topological structure with the 3-dimensional magnetic reconnection, and solar flares has attracted more and more attention. In this paper, using the theory of QSL we investigate a C5.7 classical two-ribbon solar flare (event 1) which occurred at AR11384 on 2011 December 26, and an M6.5 solar flare (event 2) which occurred at AR12371 on 2015 June 22, respectively. Combining the multi-wavelength data of AIA (Atmospheric Imaging Assembly) and vector magnetogrames of HMI (Helioseismic and Magnetic Imager) onboard SDO (Solar Dynamics Observatory), we extrapolate the coronal magnetic field using the PF (Potential Field) and NLFFF (Nonlinear Force Free Field) models, and calculate the evolution of the AR (Active Region) magnetic free energy. Then, we calculate the logarithmic distribution of Q-factors (magnetic squashing factor) at different heights above the solar photosphere with the results of the PF and NLFFF extrapolations, in order to determine the location of QSL. Afterward, we investigate the evolutionary relation between the QSLs at different heights above the solar photosphere and the flare ribbons observed at the corresponding heights. Finally, we study the multi-wavelength evolution features of the 2 flare events, and obtain by calculation the mean slip velocities of magnetic lines in the event 2 at 304 Å and 335 Å to be 4.6 km s^-1 and 6.3 km s^-1, respectively. We find that the calculated location of QSL in the chromosphere and corona is in good agreement with the location of flare ribbons at the same height, and the QSLs at different heights have almost the same evolutionary behavior in time as the flare ribbons of the corresponding heights, which highlights the role of QSL in the research of 3D magnetic reconnection and solar flare, and we suggest that the energy release in the flare of event 2 may be triggered by the magnetic reconnection at the place of QSL. We also suggest that the QSL is very important for us to study the essential relation between the 3D and 2D magnetic reconnections.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

SIGNATURES OF CORONAL CURRENTS IN MICROWAVE IMAGES

Microwave emission from solar active regions at frequencies above 4 GHz is dominated by gyroresonance opacity in strong coronal magnetic fields, which allows us to use radio observations to measure coronal magnetic field strengths. In this paper we demonstrate one powerful consequence of this fact: the ability to identify coronal currents from their signatures in microwave images. Specifically, we compare potential-field (i.e., current-free) extrapolations of photospheric magnetic fields with microwave images and are able to identify regions where the potential extrapolation fails to predict the magnetic field strength required to explain the microwave images. Comparison with photospheric vector magnetic field observations indicates that the location inferred for coronal currents agrees with that implied by the presence of vertical currents in the photosphere. The location, over a neutral line exhibiting strong shear, is also apparently associated with strong heating.     

Preprocessing photospheric vector magnetograms for nonlinear force-free field extrapolation of the global corona

Nonlinear force-free magnetic field(NLFFF) extrapolation based on the observed photospheric magnetic field is the most important method to obtain the coronal magnetic field nowadays.However, raw photospheric magnetograms contain magnetic forces and small-scale noises, and fail to be consistent with the force-free assumption of NLFFF models. The procedure for removing the forces and noises in observed data is called preprocessing. In this paper, we extend the preprocessing code of Jiang Feng to spherical coordinates for a full sphere. We first smooth the observed data with Gaussian smoothing, and then split the smoothed magnetic field into a potential field and a non-potential field.The potential part is computed by a numerical potential field model, and the non-potential part is preprocessed using an optimization method to minimize the magnetic forces and magnetic torques. Applying the code to synoptic charts of the vector magnetic field from SDO/HMI, we find it can effectively reduce the noises and forces, and improve the quality of data for a better input which will be used for NLFFF extrapolations applied to the global corona.     

RECONSTRUCTION OF THE THREE-DIMENSIONAL CORONAL MAGNETIC FIELD

Studies of solar flares indicate that the mechanism of flares is magnetic in character and that the coronal magnetic field is a key to understanding solar high-energy phenomena. In our ongoing research we are conducting a systematic study of a large database of observations which includes both coronal structure (from the Soft X-ray Telescope on the Yohkoh spacecraft) and photospheric vector magnetic fields (from the Haleakala Stokes Polarimeter at Mees Solar Observatory). We compare the three-dimensional nonlinear force-free coronal magnetic field, computed from photospheric boundary data, to images of coronal structure. In this paper we outline our techniques and present results for active region AR 7220/7222. We show that the computed force-free coronal magnetic field agrees well with Yohkoh X-ray coronal loops, and we discuss the properties of the coronal magnetic field and the soft X-ray loops.     

Magnetic Stereoscopy

The space mission Solar TErrestrial RElations Observatory (STEREO) will provide images from two viewpoints. An important aim of the STEREO mission is to get a 3D view of the solar corona. We develop a program for the stereoscopic reconstruction of 3D coronal loops from images taken with the two STEREO spacecraft. A pure geometric triangulation of coronal features leads to ambiguities because the dilute plasma emissions complicates the association of features in image 1 with features in image 2. As a consequence of these problems, the stereoscopic reconstruction is not unique and multiple solutions occur. We demonstrate how these ambiguities can be resolved with the help of different coronal magnetic field models (potential, linear, and non-linear force-free fields). The idea is that, due to the high conductivity in the coronal plasma, the emitting plasma outlines the magnetic field lines. Consequently, the 3D coronal magnetic field provides a proxy for the stereoscopy, which allows to eliminate inconsistent configurations. The combination of stereoscopy and magnetic modelling is more powerful than one of these tools alone. We test our method with the help of a model active region and plan to apply it to the solar case as soon as STEREO data become available.     

A statistical study on property of spatial magnetic field for solar active region

Magnetic fields dominate most solar activities, there exist direct relations between solar flare and the distributions of magnetic field, and also its corresponding magnetic energy. In this paper, the statistical results about the relationships between the spatial magnetic field and solar flare are given basing on vector magnetic field observed by the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station (HSOS). The spatial magnetic fields are obtained by extrapolated photosphere vector magnetic field observed by SMFT. There are 23 active regions with flare eruption are chosen as data samples, which were observed from 1997 to 2007. The results are as follows: 1. Magnetic field lines become lower after flare for 16 (69 %) active regions; 2. The free energy are decreased after flare for 17 (74 %) active regions. It can conclude that for most active regions the changes of magnetic field after solar flare re coincident with the previous observations and studies.     

A magnetic bald-patch flare in solar active region 11117

With SDO observations and a data-constrained magnetohydrodynamics(MHD)model,we identify a confined multi-ribbon flare that occurred on 2010 October 25 in solar active region 11117 as a magnetic bald patch(BP)flare with strong evidence.From the photospheric magnetic field observed by SDO/HMI,we find there are indeed magnetic BPs on the polarity inversion lines(PILs)which match parts of the flare ribbons.From the 3D coronal magnetic field derived from an MHD relaxation model constrained by the vector magnetograms,we find strikingly good agreement of the BP separatrix surface(BPSS)footpoints with the flare ribbons,and the BPSS itself with the hot flaring loop system.Moreover,the triggering of the BP flare can be attributed to a small flux emergence under the lobe of the BPSS,and the relevant change of coronal magnetic field through the flare is reproduced well by the pre-flare and post-flare MHD solutions,which match the corresponding pre-and post-flare AIA observations,respectively.Our work contributes to the study of non-typical flares that constitute the majority of solar flares but which cannot be explained by the standard flare model.     

Probing Twisted Magnetic Field Using Microwave Observations in an M Class Solar Flare on 11 February, 2014

This work demonstrates the possibility of magnetic-field topology investigations using microwave polarimetric observations. We study a solar flare of GOES M1.7 class that occurred on 11 February, 2014. This flare revealed a clear signature of spatial inversion of the radio-emission polarization sign. We show that the observed polarization pattern can be explained by nonthermal gyrosynchrotron emission from the twisted magnetic structure. Using observations of the Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Observatory, Radio Solar Telescope Network, and Solar Dynamics Observatory, we have determined the parameters of nonthermal electrons and thermal plasma and identified the magnetic structure where the flare energy release occurred. To reconstruct the coronal magnetic field, we use nonlinear force-free field (NLFFF) and potential magnetic-field approaches. Radio emission of nonthermal electrons is simulated by the GX Simulator code using the extrapolated magnetic field and the parameters of nonthermal electrons and thermal plasma inferred from the observations; the model radio maps and spectra are compared with observations. We have found that the potential-magnetic-field approach fails to explain the observed circular polarization pattern; on the other hand, the Stokes-\(V\) map is successfully explained by assuming nonthermal electrons to be distributed along the twisted magnetic structure determined by the NLFFF extrapolation approach. Thus, we show that the radio-polarization maps can be used for diagnosing the topology of the flare magnetic structures where nonthermal electrons are injected.     

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.     

Radio Versus EUV/X-Ray Observations of the Solar Atmosphere

This paper reviews the contrasting properties of radio and EUV/X-ray observations for the study of the solar atmosphere. The emphasis is placed on explaining the nature of radio observations to an EUV/X-ray audience. Radio emission is produced by mechanisms which are well-understood within classical physics. Bremsstrahlung tends to be dominant at low frequencies, while gyro-resonance emission from strong magnetic fields produces bright sources at higher frequencies. At most radio frequencies the images of the Sun are dominated almost everywhere by bremsstrahlung opacity, which may be optically thick or thin depending on circumstances. Where gyro-resonance sources are present they may be used as sensitive probes of the regions above active regions where magnetic field strengths exceed several hundred gauss, and this unique capability is one of the strengths of radio observations. Typically a gyro-resonance radio source shows the temperature on an optically thick surface of constant magnetic field within the corona. Since each radio frequency corresponds to a different magnetic field strength, the coronal structure can be `peeled away' by using different frequencies. The peculiarities of radio observing techniques are discussed and contrasted with EUV/X-ray techniques. Radio observations are strong at determining temperatures and coronal magnetic field strengths while EUV/X-ray observations better sense densities and reveal coronal magnetic field lines: in this way the two wavelength domains are nicely complementary.     

Coronal Magnetic Field Structure and Evolution for Flaring AR 11117 and Its Surroundings

In this study, photospheric vector magnetograms obtained with the Synoptic Optical Long-term Investigations of the Sun (SOLIS) survey are used as boundary conditions to model three-dimensional nonlinear force-free (NLFF) coronal magnetic fields as a sequence of NLFF equilibria in spherical geometry. We study the coronal magnetic field structure inside an active region and its temporal evolution. We compare the magnetic field configuration obtained from NLFF extrapolation before and after the flaring event in active region (AR) 11117 and its surroundings observed on 27 October 2010, and we also compare the magnetic field topologies and the magnetic energy densities and study the connectivities between AR 11117 and its surroundings. During the investigated time period, we estimate the change in free magnetic energy from before to after the flare to be 1.74×10³²?erg, which represents about 13.5?% of the NLFF magnetic energy before the flare. In this study, we find that electric currents from AR 11117 to its surroundings were disrupted after the flare.     

A Rapid, Manual Method to Map Coronal-Loop Structures of an Active Region Using Cubic Bézier Curves and Its Applications to Misalignment Angle Analysis

A rapid and flexible manual method is described that maps individual coronal loops of a 2D EUV image as Bézier curves using only four points per loop. Using the coronal loops as surrogates of magnetic-field lines, the mapping results restrict the magnetic-field models derived from extrapolations of magnetograms to those admissible and inadmissible via a fitness parameter. We outline explicitly how the coronal loops can be employed in constraining competing magnetic-field models by transforming 2D coronal-loop images into 3D field lines. The magnetic-field extrapolations must satisfy not only the lower boundary conditions of the vector field (the vector magnetogram) but also must have a set of field lines that satisfies the mapped coronal loops in the volume, analogous to an upper boundary condition. This method uses the minimization of the misalignment angles between the magnetic-field model and the best set of 3D field lines that match a set of closed coronal loops. The presented method is an important tool in determining the fitness of magnetic-field models for the solar atmosphere. The magnetic-field structure is crucial in determining the overall dynamics of the solar atmosphere.     

Modulational instability of self-generated magnetic fields

It is shown analytically that self-generated magnetic fields are modulationally unstable with respect to the uniform state of a plasma; such an instability would localize the magnetic field. This localized magnetic flux may well produce small-scale intermittent magnetic fields in coronal active regions or solar flares.     

Topology of Magnetic Field and Coronal Heating in Solar Active Regions – II. The Role of Quasi-Separatrix Layers

The photospheric vector magnetic fields, H and soft X-ray images of AR 7321 were simultaneously observed with the Solar Flare Telescope at Mitaka and the Soft X-ray Telescope of Yohkoh on October 26, 1992, when there was no important activity in this region. Taking the observed photospheric vector magnetic fields as the boundary condition, 3D magnetic fields above the photosphere were computed with a new numerical technique. Then quasi-separatrix layers (QSLs), i.e., regions where 3D magnetic reconnection takes place, were determined in the computed 3D magnetic fields. Since Yohkoh data and Mitaka data were obtained in well-arranged time sequences during the day, the evolution of 3D fields, H features and soft X-ray features in this region can be studied in detail. Through a comparison among the 3D magnetic fields, H features and soft X-ray features, the following results have been obtained: (a) H plages are associated with the portions of QSLs in the chromosphere; (b) diffuse coronal features (DCFs) and bright coronal features (BCFs) are morphologically confined by the coronal linkage of the field lines related to the QSLs; (c) BCFs are associated with a part of the magnetic field lines related to the QSLs. These results suggest that as the likely places where energy release may occur by 3D magnetic reconnection, QSLs play an important role in the chromospheric and coronal heating in this active region.     

On the comparison of radio-astronomical measurements of the height structure of magnetic field with results of model approximations

The results of microwave observations of the polarized emission of active regionsmade with the RATAN-600 radio telescope are used to develop the method for determining the structure of the magnetic field of these regions at coronal heights. About 1000-G-strong magnetic fields are observed in the solar atmosphere at rather high altitudes (from 10 to 25 Mm). This result is confirmed fairly well by the ultraviolet observations of magnetic loops, it is consistent with earlier radio-astronomical observations of the magnetic field at the height of the transition region, and it corresponds as well, if interpreted in terms of the dipole magnetic field model, to the vertical gradients of the photospheric magnetic field.