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.     

Determining the 3D Structure of the Corona Using Vertical Height Constraints on Observed Active Region Loops

The corona associated with an active region is structured by high-temperature, magnetically dominated closed and open loops. The projected 2D geometry of these loops is captured in EUV filtergrams. In this study using SDO/AIA 171 Å filtergrams, we expand our previous method to derive the 3D structure of these loops, independent of heliostereoscopy. We employ an automated loop recognition scheme (Occult-2) and fit the extracted loops with 2D cubic Bézier splines. Utilizing SDO/HMI magnetograms, we extrapolate the magnetic field to obtain simple field models within a rectangular cuboid. Using these models, we minimize the misalignment angle with respect to Bézier control points to extend the splines to 3D (Gary, Hu, and Lee 2014). The derived Bézier control points give the 3D structure of the fitted loops. We demonstrate the process by deriving the position of 3D coronal loops in three active regions (AR 11117, AR 11158, and AR 11283). The numerical minimization process converges and produces 3D curves which are consistent with the height of the loop structures when the active region is seen on the limb. From this we conclude that the method can be important in both determining estimates of the 3D magnetic field structure and determining the best magnetic model among competing advanced magnetohydrodynamics or force-free magnetic-field computer simulations.     

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.     

Real and virtual unipolar regions

Difficulties in relating magnetograph measurements to the actual solar magnetic field are discussed. After a brief review both of problems inherent in the nature of the measurements and of sources of instrumental error, we show that field measurements taken within the photosphere can map out large-scale regions of a single magnetic polarity even though these regions contain no footpoints of large-scale magnetic structures, but instead only aggregates of small, unresolved bipoles. This may occur wherever the density of unresolved bipoles has a preferred orientation and a spatial variation along the direction of that orientation. We call these regionsvirtual unipolar regions, as they are not connected to regions of opposite polarity by field loops or lines passing through the corona. Investigation of these regions shows that they can arise at widely separated locations, and that they may evolve into real unipolar magnetic regions which are connected to the chromospheric and coronal fields. These results can explain a number of puzzling aspects of magnetograph observations of the solar background magnetic field.     

Nonlinear Force-Free and Potential-Field Models of?Active-Region and Global Coronal Fields during?the?Whole Heliosphere Interval

Between 24 March 2008 and 2 April 2008, the three active regions (ARs) NOAA 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliosphere Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer-belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions.     

Helicity Patterns of the Active Regions Connected by Transequatorial Loops

Using photospheric vector magnetograms of the Huairou Solar Observing Station and coronal X-ray images from the Yohkoh Soft X-Ray Telescope, we calculate the helicity patterns of 43 pairs of active regions and the chirality of 50 pairs of opposite magnetic polarity regions that are connected by transequatorial loops (TLs). To make the results more convincing, two helicity proxies including the local current helicity h _c and the force-free factor α _best are computed. The results, which are similar for both parameters, are as follows: (1) Current helicity of the active regions pairs connected by transequatorial loops have no obvious regularity: About 50% of the active region pairs carry the same current helicity sign and about 50% of them have the opposite. (2) If we consider the magnetic polarity pairs connected by the TLs, the result is almost the same as that for the active region pairs, with a little more than half of them showing the same chirality. We also make linear force-free extrapolations for 33 TLs and determine their force-free parameter α by comparing extrapolated field lines to X-ray images of the TLs. Out of the 19 cases when the footpoints of the TLs have the same current helicity sign, we find that the sign of α of the TLs is the same as the sign of the current helicity in the footpoints in 12 cases, whereas it is of opposite sign in 4 cases, and in 3 cases the TLs were found to be potential.     

Dynamics of charged dust particles in protoplanetary discs

We study the effect of an imposed magnetic field on the motion of charged dust particles in magnetically active regions of a protoplanetary disc. Assuming a power law structure for the vertical and the toroidal components of the magnetic field for the regions beyond magnetically dead region of the disc, the radial and the vertical velocities of the charged particles, in the asymptotic case of small particles, are calculated analytically. While grains with radii smaller than a critical radius significantly are affected by the magnetic force, motion of the particles with larger radii is independent of the magnetic field. The critical radius depends on the magnetic geometry and the charge of the grains. Assuming that a grain particle has one elementary charge and the physical properties of the disc correspond to a minimum-mass solar nebula, we show that only micron-sized grains are affected by the magnetic force. Also, charge polarity determines direction of the radial velocity. For such small particles, both the radial and the vertical velocities increase due to the magnetic force.     

Flux Ropes Embedded In A Radial Magnetic Field: Analytic Solutions For The External Magnetic Field

Three sympathetic flares were observed with the Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station of Beijing Astronomical Observatory on 29 August, and 1 September 1990. Each set of sympathetic flares had three ribbons. Two ribbons appeared in active region NOAA 6233 and one ribbon occurred in NOAA 6240 embedded in a single polarity area. Photospheric vector magnetograms were simultaneously obtained from both regions as well. We use a new numerical technique to reconstruct the chromospheric and coronal magnetic fields by making use of the observed vector magnetic fields in the photosphere as boundary conditions. Magnetic field loops linking both regions were identified from the reconstructed 3-D fields. The analysis of chromospheric filtergrams and reconstructed 3-D magnetic fields indicates that interaction between a sheared lower loop in the active region NOAA 6233 and a higher loop linking the two regions resulted in sympathetic flares. The analysis of the time delay between flare ribbons in NOAA 6233 and 6240 indicates that heat conduction along the higher loop from the primary energy release site is responsible for the sympathetic flaring in NOAA 6240. The events reported in this paper represent only one alternative as the cause of sympathetic flaring in which energy transport along coronal interconnecting loops plays the major role, and no in-situ energy release is required.     

Type-II Bursts in Meter and Deca – Hectometer Wavelengths and Their Relation to Flares and CMEs: II

Solar coronal holes (CHs) are large regions of the corona magnetically open to interplanetary space. The nearly rigid north?–?south CH boundaries (CHBs) of equatorward extensions of polar CHs are maintained while the underlying photospheric fields rotate differentially, so interchange magnetic reconnection is presumed to be occurring continually at the CHBs. The time and size scales of the required reconnection events at CHBs have not been established from previous observations with soft X-ray images. We use TRACE 195 Å observations on 9 December 2000 of a long-lived equatorial extension of the negative-polarity north polar CH to look for changes of ??5 arcsec to >?20 arcsec at the western CHB. Brightenings and dimmings are observed on both short (≈?5 minutes) and long (≈?7 hours) time scales, but the CHB maintains its quasi-rigid location. The transient CHB changes do not appear associated with either magnetic field enhancements or the changes in those field enhancements observed in magnetograms from the Michelson Doppler Imager (MDI) on SOHO. In seven hours of TRACE observations we find no examples of the energetic jets similar to those observed to occur in magnetic reconnection in polar plumes. The lack of dramatic changes in the diffuse CHB implies that gradual magnetic reconnection occurs high in the corona with large (??10°) loops and/or weak coronal fields. We compare our results with recent observations of active regions at CHBs. We also discuss how the magnetic polarity symmetry surrounding quasi-rigid CHs implies an asymmetry in the interchange reconnection process and a possible asymmetry in the solar wind composition from the eastern and western CHB source regions.     

Outflows at the Edges of an Active Region in a Coronal Hole: A Signature of Active Region Expansion?

Outflows of plasma at the edges of active regions surrounded by quiet Sun are now a common observation with the Hinode satellite. While there is observational evidence to suggest that the outflows are originating in the magnetic field surrounding the active regions, there is no conclusive evidence that reveals how they are driven. Motivated by observations of outflows at the periphery of a mature active region embedded in a coronal hole, we have used a three-dimensional simulation to emulate the active region’s development in order to investigate the origin and driver of these outflows. We find that outflows are accelerated from a site in the coronal hole magnetic field immediately surrounding the active region and are channelled along the coronal hole field as they rise through the atmosphere. The plasma is accelerated simply as a result of the active region expanding horizontally as it develops. Many of the characteristics of the outflows generated in the simulation are consistent with those of observed outflows: velocities up to 45 km s⁻¹, properties akin to the coronal hole, proximity to the active region’s draining loops, expansion with height, and projection over monopolar photospheric magnetic concentrations. Although the horizontal expansion occurs as a consequence of the active region’s development in the simulation, expansion is also a general feature of established active regions. Hence, it is entirely possible and plausible that the expansion acceleration mechanism displayed in the simulation is occurring in active regions on the Sun and, in addition to reconnection, is driving the outflows observed at their edges.     

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.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

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.     

How are Emerging Flux,Flares and CMEs Related to Magnetic Polarity Imbalance in Midi Data?

In order to understand whether major flares or coronal mass ejections (CMEs) can be related to changes in the longitudinal photospheric magnetic field, we study 4 young active regions during seven days of their disk passage. This time period precludes any biases which may be introduced in studies that look at the field evolution during the short-term flare or CME period only. Data from the Michelson Doppler Imager (MDI) with a time cadence of 96 min are used. Corrections are made to the data to account for area foreshortening and angle between line of sight and field direction, and also the underestimation of the flux densities. We make a systematic study of the evolution of the longitudinal magnetic field, and analyze flare and CME occurrence in the magnetic evolution. We find that the majority of CMEs and flares occur during or after new flux emergence. The flux in all four active regions is observed to have deviations from polarity balance both on the long term (solar rotation) and on the short term (few hours). The long-term imbalance is not due to linkage outside the active region; it is primarily related to the east–west distance from central meridian, with the sign of polarity closer to the limb dominating. The sequence of short-term imbalances are not closely linked to CMEs and flares and no permanent imbalance remains after them. We propose that both kinds of imbalance are due to the presence of a horizontal field component (parallel to the photospheric surface) in the emerging flux.     

VERY LARGE ARRAY OBSERVATIONS OF EVOLVING NOISE STORM SOURCES ON THE SUN

The presence of coronal magnetic fields connecting active regions is inferred from decimetric observations of solar noise storms with the Very Large Array (VLA) and from soft X-ray images taken by Yohkoh. Temporal changes in the noise storms appear to be correlated with some soft X-ray bursts detected by both Yohkoh and the GOES satellite. Combined analysis of the radio and X-ray data suggests a re-arrangement of the coronal magnetic field during the onset of impulsive noise storm burst emission. On one day during the combined VLA–Yohkoh–GOES observations, two widely-separated active regions appear to be connected by a faint trans-equatorial 91 cm source as well as two distinct soft X-ray loops. The two active regions show anti-correlated fluctuations in decimetric radio emission. On another day of combined VLA–Yohkoh observations, a series of 91 cm noise storm bursts are observed along the major axis of the associated noise storm continuum. Time sequences of Yohkoh soft X-ray images show a contraction of coronal loops prior to the onset of this series of bursts and a corresponding increase in the X-ray flux in the apparent footpoint of the overarching loop containing the noise storm. These observations imply that energy from a realignment of the magnetic field is being transferred, possibly by accelerated particles, along loops connecting separated active regions on the Sun.     

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.     

Comparison of STEREO/EUVI Loops with Potential Magnetic Field Models

The Solar Terrestrial Relations Observatory (STEREO) provides the first opportunity to triangulate the three-dimensional coordinates of active region loops simultaneously from two different vantage points in space. Three-dimensional coordinates of the coronal magnetic field have been calculated with theoretical magnetic field models for decades, but it is only with the recent availability of STEREO data that a rigorous, quantitative comparison between observed loop geometries and theoretical magnetic field models can be performed. Such a comparison provides a valuable opportunity to assess the validity of theoretical magnetic field models. Here we measure the misalignment angles between model magnetic fields and observed coronal loops in three active regions, as observed with the Extreme Ultraviolet Imager (EUVI) on STEREO on 30 April, 9 May, and 19 May 2007. We perform stereoscopic triangulation of some 100?–?200 EUVI loops in each active region and compute extrapolated magnetic field lines using magnetogram information from the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). We examine two different magnetic extrapolation methods: (1) a potential field and (2) a radially stretched potential field that conserves the magnetic divergence. We find considerable disagreement between each theoretical model and the observed loop geometries, with an average misalignment angle on the order of 20°?–?40°. We conclude that there is a need for either more suitable (coronal rather than photospheric) magnetic field measurements or more realistic field extrapolation models.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

A Framework for Understanding the Topology of Complex Coronal Structures

The Sun's coronal magnetic field is highly complex and provides the driving force for many dynamical processes. The topology of this complex field is made up mainly of discrete topological building blocks produced by small numbers of magnetic fragments. In this work we develop a method for predicting the possible topologies due to a potential field produced by three photospheric sources, and describe how this model accurately predicts the results of Brown and Priest (1999). We then sketch how this idea may be extended to more general non-symmetric configurations. It is found that, for the case of positive total flux, a local separator bifurcation may take place with three positive sources or with one positive and two negative sources, but not for two positive sources and one negative.     

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.