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.     

Discussion on the coronal structure related to type III bursts

Some statements recently published on the coronal structure related to type III bursts are discussed. The indirect approach based upon computed coronal magnetic field, as proposed by Kuiper (1973), is examined; it is concluded that some doubt exists about the suitability of this method. The problem of the relationship between the existence of filaments inside an active center and type III bursts production is analysed: considering the respective locations of flaring sites and filaments as well as their place inside the magnetic network of the active center, one cannot deduce any evidence of type III inhibition by filaments. There is no direct conclusive evidence of the association of type III's with known coronal structures. Some observations suggest that at least in some cases, the coronal streamers are involved.     

Modeling coronal magnetic field using spherical geometry: cases with several active regions

The magnetic fields in the solar atmosphere structure the plasma, store free magnetic energy and produce a wide variety of active solar phenomena, like flare and coronal mass ejections (CMEs). The distribution and strength of magnetic fields are routinely measured in the solar surface (photosphere). Therefore, there is considerable interest in accurately modeling the 3D structure of the coronal magnetic field using photospheric vector magnetograms. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Nonlinear force-free field (NLFFF) models are thought to be viable tools for those task. Usually those models use Cartesian geometry. However, the spherical nature of the solar surface cannot be neglected when the field of view is large. In this work, we model the coronal magnetic field above multiple active regions using NLFFF extrapolation code using vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph (VSM) as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with their respective coronal EUV-images from the Atmospheric Imaging Assembly (SDO/AIA) observed on October 15, 2011 and November 13, 2012. This study has found that the NLFFF model in spherical geometry reconstructs the magnetic configurations for several active regions which agrees to some extent with observations. During October 15, 2011 observation, there are substantial number of trans-equatorial loops carrying electric current.     

Open magnetic fields and the solar cycle

Models of open magnetic structures on the Sun are presented for periods near solar minimum (CR 1626–1634) and near solar maximum (CR 1668–1678). Together with previous models of open magnetic structures during the declining phase (CR 1601–1611) these calculations provide clues to the relations between open structures, coronal holes, and active regions at different times of the solar cycle. Near solar minimum the close relation between active regions and open structures does not exist. It is suggested that near solar minimum the systematic emergence of new flux with the proper polarity imbalance to maintain open magnetic structures may occur primarily at very small spatial scales. Near solar maximum the role of active regions in maintaining open structures and coronal holes is strong, with large active regions emerging in the proper location and orientation to maintain open structures longer than typical active region lifetimes. Although the use of He I 10830 Å spectroheliograms as a coronal hole indicator is shown to be subject to significant ambiguity, the agreement between calculated open structures and coronal holes determined from He I 10830 Å spectroheliograms is very good. The rotation properties of calculated open structures near solar maximum strongly suggest two classes of features: one that rotates differentially similar to sunspots and active regions and a separate class that rotates more rigidly, as was the case for single large coronal holes during Skylab.     

Longitudinal Distribution of Coronal Holes During 1976–2002

The longitudinal distribution of coronal holes has been analyzed for the time interval 1976–2002. Coronal holes don't seem to be randomly distributed. The cluster structure has been revealed in the time—space organization of coronal hole distribution. The complexity and lifetime of clusters depend on the solar cycle phase. The comparison of active region and coronal hole cluster structures shows that some coronal hole clusters as well as active region ones occur almost simultaneously in both hemispheres, some clusters in the north or in the south hemisphere only. Some coronal hole clusters coincide with the active region clusters and some do not coincide. They reflect the large-scale solar magnetic field distribution.     

Magnetic Energy Storage and Current Density Distributions for Different Force-Free Models

In the last decades, force-free-field modelling has been used extensively to describe the coronal magnetic field and to better understand the physics of solar eruptions at different scales. Especially the evolution of active regions has been studied by successive equilibria in which each computed magnetic configuration is subject to an evolving photospheric distribution of magnetic field and/or electric-current density. This technique of successive equilibria has been successful in describing the rate of change of the energetics for observed active regions. Nevertheless the change in magnetic configuration due to the increase/decrease of electric current for different force-free models (potential, linear and nonlinear force-free fields) has never been studied in detail before. Here we focus especially on the evolution of the free magnetic energy, the location of the excess of energy, and the distribution of electric currents in the corona. For this purpose, we use an idealised active region characterised by four main polarities and a satellite polarity, allowing us to specify a complex topology and sheared arcades to the coronal magnetic field but no twisted flux bundles. We investigate the changes in the geometry and connectivity of field lines, the magnetic energy and current-density content as well as the evolution of null points. Increasing the photospheric current density in the magnetic configuration does not dramatically change the energy-storage processes within the active region even if the magnetic topology is slightly modified. We conclude that for reasonable values of the photospheric current density (the force-free parameter α<0.25 Mm⁻¹), the magnetic configurations studied do change but not dramatically: i) the original null point stays nearly at the same location, ii) the field-line geometry and connectivity are slightly modified, iii) even if the free magnetic energy is significantly increased, the energy storage happens at the same location. This extensive study of different force-free models for a simple magnetic configuration shows that some topological elements of an observed active region, such as null points, can be reproduced with confidence only by considering the potential-field approximation. This study is a preliminary work aiming at understanding the effects of electric currents generated by characteristic photospheric motions on the structure and evolution of the coronal magnetic field.     

Magnetic arcades in stellar coronae I. Cylindrical geometry

X-ray spectroscopy performed by different astronomical spacecrafts has shown that many active late-type stars possess coronae. For such reason, the magnetic structure of stellar coronae has raised considerable interest and, by analogy with the Sun, it is generally assumed that stellar coronae are structured by magnetic fields having the shape of arcades. Most of those coronal magnetic field configurations assume translational symmetry and are based in planar source surfaces. However, as soon as either the length or the width of such source surfaces become non negligible as compared to the stellar radius, the application of the cylindrical geometry seems to be more appropriate. Then, one way of obtaining coronal magnetic configurations is to deal with source domains extended over a cylindrical surface. In this paper we generate potential coronal arcades based on cylindrical source surfaces with non negligible length or width compared to the stellar radius. The flux function, the magnetic field components, the shape of magnetic field lines and other characteristic magnitudes have been obtained and analyzed for both cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

A Numerical Study of the Response of the Coronal Magnetic Field to Flux Emergence

Large-scale solar eruptions, known as coronal mass ejections (CMEs), are regarded as the main drivers of space weather. The exact trigger mechanism of these violent events is still not completely clear; however, the solar magnetic field indisputably plays a crucial role in the onset of CMEs. The strength and morphology of the solar magnetic field are expected to have a decisive effect on CME properties, such as size and speed. This study aims to investigate the evolution of a magnetic configuration when driven by the emergence of new magnetic flux in order to get a better insight into the onset of CMEs and their magnetic structure. The three-dimensional, time-dependent equations for ideal magnetohydrodynamics are numerically solved on a spherical mesh. New flux emergence in a bipolar active region causes destabilisation of the initial stationary structure, finally resulting in an eruption. The initial magnetic topology is suitable for the ??breakout?? CME scenario to work. Although no magnetic flux rope structure is present in the initial condition, highly twisted magnetic field lines are formed during the evolution of the system as a result of internal reconnection due to the interaction of the active region magnetic field with the ambient field. The magnetic energy built up in the system and the final speed of the CME depend on the strength of the overlying magnetic field, the flux emergence rate, and the total amount of emerged flux. The interaction with the global coronal field makes the eruption a large-scale event, involving distant parts of the solar surface.     

Nonlinear Force-Free Extrapolation of Emerging Flux with a Global Twist and Serpentine Fine Structures

We study the flux emergence process in NOAA active region 11024, between 29 June and 7 July 2009, by means of multi-wavelength observations and nonlinear force-free extrapolation. The main aim is to extend previous investigations by combining, as much as possible, high spatial resolution observations to test our present understanding of small-scale (undulatory) flux emergence, whilst putting these small-scale events in the context of the global evolution of the active region. The combination of these techniques allows us to follow the whole process, from the first appearance of the bipolar axial field on the east limb, until the buoyancy instability could set in and raise the main body of the twisted flux tube through the photosphere, forming magnetic tongues and signatures of serpentine field, until the simplification of the magnetic structure into a main bipole by the time the active region reaches the west limb. At the crucial time of the main emergence phase high spatial resolution spectropolarimetric measurements of the photospheric field are employed to reconstruct the three-dimensional structure of the nonlinear force-free coronal field, which is then used to test the current understanding of flux emergence processes. In particular, knowledge of the coronal connectivity confirms the identity of the magnetic tongues as seen in their photospheric signatures, and it exemplifies how the twisted flux, which is emerging on small scales in the form of a sea-serpent, is subsequently rearranged by reconnection into the large-scale field of the active region. In this way, the multi-wavelength observations combined with a nonlinear force-free extrapolation provide a coherent picture of the emergence process of small-scale magnetic bipoles, which subsequently reconnect to form a large-scale structure in the corona.     

太阳多极活动区中的磁重联、剪切低磁弧内的强电流和冕穴结构

探讨了复杂磁结构上空日冕物理状态与磁剪切的关系．结果表明在强磁场的磁中性线上方磁剪切会引起具有强电流和较强等离子体压力的低磁弧．这可解释Ｙｏｈｋｏｈ 卫星的观测结果     

Latent Heating of Coronal Loops

This paper is aimed at establishing the relationship between the large-scale magnetic fields (LSMF), coronal holes (CH), and active regions (AR) in the Sun. The LSMF structure was analyzed by calculating the vector photospheric magnetic field under a potential approximation. Synoptic maps were drawn to study the distribution of the B field component and to isolate regions where the open field lines of the unipolar magnetic field are most radial. These are the sites of occurrence of X-ray and Hei 10830 Å coronal holes detected from the SXT/Yohkoh images. It is shown that coronal holes are usually located in LSMF regions with a typical pattern of divergentB vectors and a so-called saddle configuration.B vectors from the conjugate (spaced by 90°) coronal holes converge towards the active regions between CH. Variations in AR distort coronal holes and change their boundaries. This implies that the energy regime in CH depends on the energy supply from the active region. The LSMF structure is more stable than coronal holes, remaining practically unchanged during tens of rotations of the Sun. Thus, a peculiar magnetically coupled system of LSMF/CH/AR has been revealed. A model has been suggested to describe the interaction of the emerging toroids in the convection zone and in the photosphere. The cellular convection, that develops at the center of the toroids, is responsible for the occurrence of active regions. The model qualitatively describes the observed particularities of the LSMF/CH/AR system.     

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 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.     

Coronal Mass Ejections and the Index of Effective Solar Multipole

The paper considers the relationship between the cyclic variations in the velocity of coronal mass ejections (CME) and the large-scale magnetic field structure (LSMF) in cycles 21??C?23. To characterize a typical size of the LSMF structure, we have used the index of the effective solar multipole (ESMI). The cyclic behavior of the CME occurrence rate and velocity proved to be similar to that of ESMI. The hysteresis observed in variations of the CME maximum velocity is interpreted as a manifestation of different contributions from the two field structures (local and global magnetic fields) in different phases of the 11-year activity cycle. It is suggested that cyclic variations in the maximum velocity of coronal mass ejections are due to different conditions for the formation of the complexes of active regions connected by coronal arch systems, which are the main source of high-velocity CMEs.     

Interpretation of multiwavelength observations of November 5, 1980 solar flares by the magnetic topology of AR 2766

We present a detailed analysis of the magnetic topology of AR 2776 together with Hα UV, X-rays, and radio observations of the November 5, 1980 flares in order to understand the role of the active region large-scale topology on the flare process. As at present the coronal magnetic field is modeled by an ensemble of sub-photospheric sources whose positions and intensities are deduced from a least-square fit between the computed and observed longitudinal magnetic fields. Charges and dipole representations are shown to lead to similar modeling of the magnetic topology provided that the number of sources is great enough. However, for AR 2776, departure from a potential field has to be taken into account, therefore a linear force-free field extrapolation is used. The locations of the four bright off-band Hα kernels in quadrupolar active regions have been studied previously. In this new study the active region is bipolar and shows a two-ribbon structure. We show that these two ribbons are a consequence of the bipolar photospheric field (the four kernels of quadrupolar regions merge into two bipolar regions). The two ribbons are found to be located at the intersection of the separatrices with the chromosphere when the shear, deduced from the fibril direction, is taken into account. This study supports the hypothesis that magnetic energy is stored in field-aligned currents and released by magnetic reconnection at the location of the separator, before being transported along field lines to the chromospheric level. It is also possible that part of the magnetic energy could be stored and released on the separatrices. Our study shows that meeting just one of two conditions- the presence of intense coronal currents or of a separator in a magnetic field configuration - is not sufficient for flaring. In order to release the stored energy, the coronal currents need either to be formed along the separatrices or to be transported towards the separator or separatrices. The location of the observed photospheric current concentrations on the computed separatrices supports this view. Member of the Carrera del Investigador Científico, CONICET.     

Investigation of the evolution of coronal bright points and magnetic field topology

Our investigation has been carried using the instruments onboard the Solar Dynamics Observatory (SDO) providing a high resolution of images (AIA photographs and HMI magnetograms). We have investigated the structure and magnetic evolution of several coronal bright points and small scale N-S polarity magnetic fluxes closely associated with them. We also compare the evolution of the magnetic polarities of elementary isolated sources of positive and negative fluxes (magnetic bipoles) and coronal bright points. Tiny (“elementary”) coronal bright points have been detected. A standard coronal bright point is shown to be a group of “elementary” coronal bright points that flare up sequentially. Our investigation shows that a change in the magnetic fluxes of opposite polarities is observed before the flare of a coronal bright point. We show that not all cases of the formation of coronal bright points are described by the magnetic reconnection model. This result has not been considered previously and has not been pointed out by other authors.     

Determining the Intrinsic CME Flux Rope Type Using Remote-sensing Solar Disk Observations

A key aim in space weather research is to be able to use remote-sensing observations of the solar atmosphere to extend the lead time of predicting the geoeffectiveness of a coronal mass ejection (CME). In order to achieve this, the magnetic structure of the CME as it leaves the Sun must be known. In this article we address this issue by developing a method to determine the intrinsic flux rope type of a CME solely from solar disk observations. We use several well-known proxies for the magnetic helicity sign, the axis orientation, and the axial magnetic field direction to predict the magnetic structure of the interplanetary flux rope. We present two case studies: the 2 June 2011 and the 14 June 2012 CMEs. Both of these events erupted from an active region, and despite having clear in situ counterparts, their eruption characteristics were relatively complex. The first event was associated with an active region filament that erupted in two stages, while for the other event the eruption originated from a relatively high coronal altitude and the source region did not feature a filament. Our magnetic helicity sign proxies include the analysis of magnetic tongues, soft X-ray and/or extreme-ultraviolet sigmoids, coronal arcade skew, filament emission and absorption threads, and filament rotation. Since the inclination of the post-eruption arcades was not clear, we use the tilt of the polarity inversion line to determine the flux rope axis orientation and coronal dimmings to determine the flux rope footpoints, and therefore, the direction of the axial magnetic field. The comparison of the estimated intrinsic flux rope structure to in situ observations at the Lagrangian point L1 indicated a good agreement with the predictions. Our results highlight the flux rope type determination techniques that are particularly useful for active region eruptions, where most geoeffective CMEs originate.     

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.     

日冕磁场重建方法在研究太阳爆发活动中的应用

太阳是与地球关系最为密切的天体.发生在日面上的剧烈爆发性活动可能对人类的生存环境产生巨大影响甚至是灾难性后果.包含太阳耀斑、暗条爆发和日冕物质抛射在内的太阳爆发活动是同一物理过程的不同表现形式,其能量来源于爆发前储存在日冕中的磁场自由能.因此,了解日冕磁场的3维结构是理解太阳爆发的触发机制以及活动区的稳定性等现象的前提.由于观测技术限制,目前尚无法对日冕磁场进行常规观测,因此发展了多种利用可常规观测的光球磁场来重建日冕磁场的方法.主要评述近10 yr来各种日冕磁场重建方法在研究太阳爆发活动中的应用.