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.     

Comparison of Five Numerical Codes for Automated Tracing of Coronal Loops

The three-dimensional (3D) modeling of coronal loops and filaments requires algorithms that automatically trace curvilinear features in solar EUV or soft X-ray images. We compare five existing algorithms that have been developed and customized to trace curvilinear features in solar images: i) the oriented-connectivity method (OCM), which is an extension of the Strous pixel-labeling algorithm (developed by Lee, Newman, and Gary); ii) the dynamic aperture-based loop-segmentation method (developed by Lee, Newman, and Gary); iii) unbiased detection of curvilinear structures (developed by Steger, Raghupathy, and Smith); iv) the oriented-direction method (developed by Aschwanden); and v) ridge detection by automated scaling (developed by Inhester). We test the five existing numerical codes with a TRACE image that shows a bipolar active region and contains over 100 discernable loops. We evaluate the performance of the five codes by comparing the cumulative distribution of loop lengths, the median and maximum loop length, the completeness or detection efficiency, the accuracy, and flux sensitivity. These algorithms are useful for the reconstruction of the 3D geometry of coronal loops from stereoscopic observations with the STEREO spacecraft, or for quantitative comparisons of observed EUV loop geometries with (nonlinear force-free) magnetic field extrapolation models.     

Extraction of Solar Coronal Magnetic Loops with the Directional 2D Morlet Wavelet Transform

We present an automated extraction method based on the continuous wavelet transform (CWT) for analyzing solar magnetic loops. The aim of the work is to extract, from the images taken from solar EUV telescopes, the traces of bright loops presumably shaped by the magnetic field of the solar corona. The technique is that of wavelet analysis, using the two-dimensional Morlet wavelet, because of its efficiency in detecting oriented features, which allows us to follow closely the curvature of the loops. Next, we segment the wavelet modulus image and we threshold it, both globally and locally (i.e., adaptively), in order to eliminate the remaining noise. Altogether, our method performs well, it is robust and fast, and could be used as a standard tool for analyzing large data sets expected from missions like SDO.     

Automated Detection of Coronal Loops Using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the automated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximize completeness, while minimizing detection of noise. For a test coronal image, we compare the global statistics (e.g. number of loops at each length) to previous automated coronal-loop detection algorithms.     

Three-Dimensional Nonlinear Force-Free Field Reconstruction of Solar Active Region 11158 by Direct Boundary Integral Equation

A three-dimensional coronal magnetic field is reconstructed for the NOAA active region 11158 on 14 February 2011. A GPU-accelerated direct boundary integral equation (DBIE) method is implemented which is approximately 1000 times faster than the original DBIE used on solar non-linear force-free field modeling. Using the SDO/HMI vector magnetogram as the bottom boundary condition, the reconstructed magnetic field lines are compared with the projected EUV loop structures as observed in the front-view (SDO/AIA) and the side-view (STEREO-A/B) images for the first time; they show very good agreement three-dimensionally. A quantitative comparison with some stereoscopically reconstructed coronal loops shows that the average misalignment angles in our model are at the same order as the state-of-the-art results obtained from reconstructed coronal loops. It is found that the observed coronal loop structures can be grouped into a number of closed and open field structures with some central bright coronal loop features around the polarity inversion line. The reconstructed highly sheared magnetic field lines agree very well with the low-lying sigmoidal filament along the polarity inversion line. This central low-lying magnetic field loop system must have played a key role in powering the flare. It should be noted that while a strand-like coronal feature along the polarity inversion line may be related to the filament, one cannot simply interpret all the coronal bright features along the polarity inversion line as manifestation of the filament without any stereoscopic information.     

Effects on UV lines observations of stationary plasma flows confined in coronal loops

We describe a method which uses a rather detailed model of coronal loop hosting a siphon flow as a diagnostic tool to interpret solar UV and X-ray observations in selected bands and lines. We apply the method to investigate the deviations from ionization equilibrium induced by stationary plasma flows confined in coronal loops and their effects on the UV and EUV emission lines observed by the instruments on board SOHO. We present results on the detailed synthesis of loop emission in a set of selected emission lines observed by CDS and SUMER, taking into account the non-equilibrium of ionization effects.     

RENDERING THREE-DIMENSIONAL SOLAR CORONAL STRUCTURES

An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from the Yohkoh SXT data.     

The Observational Evidence on the Loop–Loop Interaction in a Flare–CME Event on April 15, 1998

The evolution of the soft X-ray and EUV coronal loops related to the April 15, 1998 solar flare–CME event is studied with multiwavelength observations including hard X-rays (BATSE), microwaves (NoRP, CNAO) and magnetograms (SOHO/MDI), as well as images from Yohkoh/SXT and SOHO/EIT at 195 Å. It is shown that: (1) two soft X-ray and EUV loops rose, crossed and turned bright, (2) near one footpoint of these loops, the background magnetic field decreased, (3) there were similar quasi periodic oscillations in the time profiles of hard X-ray and microwave emissions, which characterized the loop–loop coalescence instability, (4) after the loop–loop reconnection, two new loops formed, the small one stayed at the original place, and the large one ejected out as part of the constructed prominence cloud. Based upon these observations, we argue that the decrease of the background magnetic field near these loops caused them to rise and approach each other, and in turn, the fast loop–loop coalescence instability took place and triggered the flare and the CME.     

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.     

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.     

Oscillations in EUV emission lines during a loop brightening

Oscillations in the emission in the ultraviolet lines of Cii, Oiv, and Mg x, detected by the Harvard College Observatory EUV spectroheliometer on Skylab are observed on August 7, 1973, during a loop brightening. The intensity of the EUV lines varies with a period of 141 s during the time of enhanced intensity of the coronal loop, lasting 10 min. The periodic oscillation is not only localized in the loop region but extends over a larger area of the active region, maintaining the same phase. We suggest that the intensity fluctuation of the EUV lines is caused by small-amplitude waves, propagating in the plasma confined in the magnetic loop and that size of the loop might be important in determining its perferential heating in the active region.On leave from the University of Torino, Italy.     

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.     

Magnetic Stereoscopy of Coronal Loops in NOAA 8891

The Solar TErrestrial RElations Observatory (STEREO) requires powerful tools for the three-dimensional (3D) reconstruction of the solar corona. Here we test such a program with data from SOHO and TRACE. By taking advantage of solar rotation, a newly developed stereoscopy tool for the reconstruction of coronal loops is applied to the solar active region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic reconstruction is composed of three steps. First, we identify loop structures in two TRACE images observed from two vantage viewpoints approximately 17 degrees apart, which corresponds to observations made about 30 hours apart. In the second step, we extrapolate the magnetic field in the corona with the linear force-free field model from the photospheric line-of-sight SOHO/MDI data. Finally, combining the extrapolated field lines and one-dimensional loop curves from two different viewpoints, we obtain the 3D loop structures with the magnetic stereoscopy tool. We demonstrate that by including the magnetic modeling this tool is more powerful than pure geometrical stereoscopy, especially in resolving the ambiguities generated by classical stereoscopy. This work will be applied to the STEREO mission in the near future.     

Dynamical Features and Evolutional Characteristics of Brightening Coronal Loops

We present a detailed study of coronal loop brightenings observed in an active region on the solar limb. These brightening loops show expanding and shrinking motions in EUV coronal line images and also show downflow along the loops in Lα and Hα images. By means of time-slice analysis of the images, we found that both the expanding and shrinking motions of the loops are not real motions of plasma but apparent motions like post-flare loops, where the loops at the different height are successively heated and cooled. From a temperature analysis, the time delay between the brightenings of hot 195 Å and cool Lα loops is found to be nearly equal to the time-scale of the conduction cooling. We conclude that these loop brightenings are sources of so called Hα coronal rains.     

Probing the Quiet Solar Atmosphere from the Photosphere to the Corona

We investigate the morphology and temporal variability of a quiet-Sun network region in different solar layers. The emission in several extreme ultraviolet (EUV) spectral lines through both raster and slot time-series, recorded by the EUV Imaging Spectrometer (EIS) on board the Hinode spacecraft is studied along with \(\mbox{H}\upalpha\) observations and high-resolution spectropolarimetric observations of the photospheric magnetic field. The photospheric magnetic field is extrapolated up to the corona, showing a multitude of large- and small-scale structures. We show for the first time that the smallest magnetic structures at both the network and internetwork contribute significantly to the emission in EUV lines, with temperatures ranging from \(8\times 10^{4}~\mbox{K}\) to \(6\times 10^{5}~\mbox{K}\). Two components of transition region emission are present, one associated with small-scale loops that do not reach coronal temperatures, and another component that acts as an interface between coronal and chromospheric plasma. Both components are associated with persistent chromospheric structures. The temporal variability of the EUV intensity at the network region is also associated with chromospheric motions, pointing to a connection between transition region and chromospheric features. Intensity enhancements in the EUV transition region lines are preferentially produced by \(\mbox{H}\upalpha\) upflows. Examination of two individual chromospheric jets shows that their evolution is associated with intensity variations in transition region and coronal temperatures.     

Extreme-Ultraviolet Flare Loop Emissions in an Eruptive Event

The TRACE/BBSO joint campaign on 27 September 1998 observed an eruptive flare event which lasted for half an hour. The observation covered several ultraviolet (UV) and extreme-ultraviolet (EUV) lines and H center and off-band emissions with very high spatial resolution. We find the EUV emissions in different stages of the flare display different characteristics. (1) During the `pre-flare' phase, when the SXR output was weak, we observed simultaneous impulsive HXR peak at 25–100 keV and strong EUV emission. (2) In the impulsive phase, when H, UV and SXR emissions were rising to the maxima, the EUV emission was very weak. (3) During the main phase, when SXR emission was decaying, a peak in the EUV emission was observed which was substantially delayed by 7 min compared to emissions from other wavelengths. Based on our observations, we propose that the `pre-flare' phase in this event was a separate energy release process rather than a mere pre-cursor of the flare, and it is likely that the `pre-flare' EUV emission was due to weak in situ heating of low-lying coronal loops. The mechanism of the EUV emission in the main phase is investigated. It is suggested that the delayed EUV emission may come from cooling of SXR loops.     

A Code for Automated Tracing of Coronal Loops Approaching Visual Perception

We develop a new numerical code with automated feature extraction, customized for tracing of coronal loops, a method we call Oriented Coronal CUrved Loop Tracing (OCCULT), which for the first time breaks even with the results of visual tracing. The method used is based on oriented-directivity tracing of curvi-linear features, but in contrast to other general feature-extraction algorithms, it is customized for solar EUV and SXR images by taking advantage of the specific property that coronal loops have large curvature radii compared with their widths. We evaluate the performance of this new code by comparing the cumulative distribution of loop lengths, the median and maximum loop lengths, the completeness of detection, and the congruency of the detected features with other numerical codes and visual tracings. We find that the new code closely approaches the results of visual perception and outperforms the other existing numerical codes. This algorithm is useful for the 3D reconstruction of the geometry, motion, and oscillations of coronal loops, with single or stereoscopic spacecraft, as well as for modeling of the loop hydrodynamics and the coronal magnetic field.     

Forward-Modeling of Doppler Shifts in EUV Spectral Lines

The interpretation of red- and blueshifts in EUV spectral observations remains a challenge that could provide important clues to the heating processes in the solar atmosphere. Hinode/EUV Imaging Spectrometer (EIS) observations near the footpoints of coronal loops show blueshifts for emission lines with temperatures above 1 MK and redshifts for lines below 1 MK. The implications are addressed through numerical modeling of loop dynamics. The simulation results are converted into synthetic EIS observations. A single one-dimensional loop cannot reproduce the observed behavior. However, persistent red- and blueshifts can be understood as a collective spectral signature of a bundle of 10 or more loops that have an average temperature of around 1 MK and evolve in a similar way: small-scale heating events occur randomly along each loop on a timescale of several minutes. Strong blueshifts are accompanied by low intensities. The power-law index of the energy distribution has a minor role in determining the average Doppler shifts.     

Multi-Wavelength Analysis of the 29 September 2002 M2.6/2N Flare

Using TRACE EUV 171 Å line, Hα line, Zürich radio, RHESSI, and HXRS observations the 29 September 2002 flare (M2.6), which occurred in AR NOAA 0134, was analyzed. Flaring structures were compared with a potential magnetic field model (field lines and quasi-separatrix layers) made from SOHO/MDI full-disk magnetogram. Series of high-resolution SOHO/MDI magnetograms and TRACE white-light images were used to find changes in the active region at the photosphere during the flare. The flare began with a rising of a small dark loop followed by the flare brightening observed in 171 Å with TRACE and Hα lines. In radio wavelengths, first type III bursts were observed 5 min prior to the start of hard X-ray emission, indicating a pre-flare coronal activity. The main hard X-ray emission peak (at 06:36 UT) was associated with the second type III burst activity and several slowly negatively drifting features, all starting from one point on the radio spectrum (probably a shock propagating through structures with different plasma parameters). After this time a huge loop formed and three minutes later it became visible in absorption both in Hα and 171 Å EUV lines. The phase of huge dark loop formation was characterized by long-lasting, slowly negatively drifting pulsations and drifting continuum. Finally, considering this huge loop as a surge an evolution of the event under study is discussed.     

Physics of an active region loop system

The structure of the active region loops is investigated by the study of a loop complex which undergoes a dramatic evacuation of most of the mass it contains. The need for continual energy deposition in loops is emphasized by the apparent cessation of energy input to the loops studied and their subsequent behavior. Estimates are made of the energy necessary to form and to maintain the loops, and of the relative importance of radiation and thermal conduction as energy loss mechanisms. Models based on the observed EUV emission are used to place limits on the size of loops seen in various lines and on the density and temperature structure. We find that the cool cores of active region loops are likely to be no more than a few hundred kilometers in radius and that several such cool threads may be imbedded in a common hot outer sheath. The primary energy loss on a large scale is radiation with thermal conduction contributing to local disturbances. There is a tendency for the development of apparently unstable condensations or knots along the length of a loop. Higher resolution observations will be necessary to confirm some of our predictions.