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The present study provides statistical information on the coronal magnetic field and intensity properties of small-scale bright and faint loops in the quiet Sun. We aim to quantitatively investigate the morphological and topological properties of the coronal magnetic field in bright and faint small-scale loops, with the former known as coronal bright points (CBPs). We analyse 126 small-scale loops using quasi-temporal imaging and line-of-sight magnetic field observations. We employ a recently developed automatic tool that uses a linear magneto-hydro-static model to compute the magnetic field in the solar atmosphere and automatically match individual magnetic field lines with small-scale loops. For most of the loops, we automatically obtain an excellent agreement of the magnetic field lines from the LMHS model and the loops seen in AIA 193 A. One stand-out result is that the magnetic field is non-potential. We obtain the typical ranges of loop heights, lengths, intensities, mean magnetic field strength along the loops and at loop tops, and magnetic field strength at loop footpoints. We find that loops below the classic chromospheric height of 1.5 Mm are flatter suggesting that non-magnetic forces (one of which is the plasma pressure) play an important role below this height. We find a strong correlation (Pearson coefficient of 0.9) between loop heights and lengths. The average intensity along the loops correlates stronger with the average magnetic field along the loops than with the field strength at loop tops. The latter correlation indicates that the energy release in the loops is more likely linked to the average magnetic field along the loops than the field strength on the loop tops. In other words, the energy is probably released all along the loops, but not just at the loop top. This result is consistent with the recent benchmarking radiative 3D MHD model of N\'obrega-Siberio etal., Comment: Accepted for publication in A&A

Two major mechanisms have been proposed to drive the solar eruptions: the ideal magnetohydrodynamic instability and the resistive magnetic reconnection. Due to the close coupling and synchronicity of the two mechanisms, it is difficult to identify their respective contribution to solar eruptions, especially to the critical rapid acceleration phase. Here, to shed light on this problem, we conduct a data-driven numerical simulation for the flux rope eruption on 2011 August 4, and quantify the contributions of the upward exhaust of the magnetic reconnection along the flaring current sheet and the work done by the large-scale Lorentz force acting on the flux rope. Major simulation results of the eruption, such as the macroscopic morphology, early kinematics of the flux rope and flare ribbons, match well with the observations. We estimate the energy converted from the magnetic slingshot above the current sheet and the large-scale Lorentz force exerting on the flux rope during the rapid acceleration phase, and find that (1) the work done by the large-scale Lorentz force is about 4.6 times higher than the former, and (2) decreased strapping force generated by the overlying field facilitates the eruption. These results indicate that the large-scale Lorentz force plays a dominant role in the rapid acceleration phase for this eruption., Comment: 12 pages, 5 figures; Accepted for publication in ApJL

We study the solar energetic particle (SEP) event observed on 9 October 2021, by multiple spacecraft including Solar Orbiter (SolO). The event was associated with an M1.6 flare, a coronal mass ejection (CME) and a shock wave. During the event, high-energy protons and electrons were recorded by multiple instruments located within a narrow longitudinal cone. An interesting aspect of the event was the multi-stage particle energization during the flare impulsive phase and also what appears to be a separate phase of electron acceleration detected at SolO after the flare maximum. We aim to investigate and identify the multiple sources of energetic electron acceleration. We utilize SEP electron observations from the Energetic Particle Detector (EPD) and hard X-ray (HXR) observations from the Spectrometer/Telescope for Imaging X-rays (STIX) on-board SolO, in combination with radio observations at a broad frequency range. We focus on establishing an association between the energetic electrons and the different HXR and radio emissions associated with the multiple acceleration episodes. We have found that the flare was able to accelerate electrons for at least 20 minutes during the nonthermal phase observed in the form of five discrete HXR pulses. We also show evidence that the shock wave has contributed to the electron acceleration during and after the impulsive flare phase. The detailed analysis of EPD electron data shows that there was a time difference in the release of low- and high-energy electrons, with the high-energy release delayed. Also, the observed electron anisotropy characteristics suggest different connectivity during the two phases of acceleration., Comment: 17 pages, 10 figures (main text). 3 pages, 3 figures (appendix). In review

Understanding structures and evolutions of the magnetic fields and plasma in multiple layers on the Sun is very important. A force-free magnetic field which is an accurate approximation of the solar corona due to the low plasma $\beta$ has been widely studied and used to model the coronal magnetic structure. While the force-freeness assumption is well satisfied in the solar corona, the lower atmosphere is not force-free given the high plasma $\beta$. Therefore, a magnetohydrostatic (MHS) equilibrium which takes into account plasma forces, such as pressure gradient and gravitational force, is considered to be more appropriate to describe the lower atmosphere. This paper reviews both analytical and numerical extrapolation methods based on the MHS assumption for calculating the magnetic fields and plasma in the solar atmosphere from measured magnetograms., Comment: accepted for publication in Science China Technological Sciences

The present study investigates a mini-filament eruption associated with cancelling magnetic fluxes. The eruption originates from a small-scale loop complex commonly known as a Coronal Bright Point (CBP). The event is uniquely recorded in both the imaging and spectroscopic data taken with IRIS. We analyse IRIS spectroscopic and slit-jaw imaging observations as well as images taken in the extreme-ultraviolet channels of AIA, and line-of-sight magnetic-field data from HMI onboard the SDO. We also employ an NLFFF relaxation approach based on the HMI magnetogram time series. We identify a strong small-scale brightening as a micro-flare in a CBP. The mini-eruption manifests with the ejection of hot (CBP loops) and cool (mini-filament) plasma recorded in both the imaging and spectroscopic data. The micro-flare is preceded by the appearance of an elongated bright feature in the IRIS slit-jaw 1400 A images located above the polarity inversion line. The micro-flare starts with an IRIS pixel size brightening and propagates bi-directionally along the elongated feature. We detect in both the spectral and imaging IRIS data and AIA data, strong flows along and at the edges of the elongated feature which we believe represent reconnection outflows. Both edges of the elongated feature that wrap around the edges of the erupting MF evolve into a J-type shape creating a sigmoid appearance. A quasi-separatrix layer (QSL) is identified in the vicinity of the polarity inversion line by computing the squashing factor Q in different horizontal planes of the NLFFF model. The QSL reconnection site has the same spectral appearance as the so-called explosive events identified by strong blue- and red-shifted emission, thus answering a long outstanding question about the true nature of this spectral phenomenon., Comment: accepted for publication in A&A, the abstract is reduced in size, for the movies contact MM

In this paper, we present multiwavelength observations of the triggering of a failed-eruptive M-class flare from the active region NOAA 11302, and investigate the possible reasons for the associated failed eruption. Photospheric observations and Non-Linear Force Free Field extrapolated coronal magnetic field revealed that the flaring region had a complex quadrupolar configuration with a pre-existing coronal null point situated above the core field. Prior to the onset of the M-class flare, we observed multiple periods of small-scale flux enhancements in GOES and RHESSI soft X-ray observations, from the location of the null point. The pre-flare configuration and evolution reported here are similar to the ones presented in the breakout model but at much lower coronal heights. The core of the flaring region was characterized by the presence of two flux ropes in a double-decker configuration. During the impulsive phase of the flare, one of the two flux ropes initially started erupting but resulted in a failed eruption. Calculation of the magnetic decay index revealed a saddle-like profile where decay index initially increased to the torus unstable limits within the heights of the flux ropes but then decreased rapidly reaching to negative values, which was most likely responsible for the failed eruption of the initially torus unstable flux rope., Comment: 10 figures, 1 table, accepted for publication in the Astrophysical Journal

Our understanding of the formation and evolution of the corona and the heliosphere is linked to our capability of properly interpreting the data from remote sensing and in-situ observations. In this respect, being able to correctly connect in-situ observations with their source regions on the Sun is the key for solving this problem. In this work we aim at testing a diagnostics method for this connectivity. This paper makes use of a coronal jet observed on 2010 August 2nd in active region 11092 as a test for our connectivity method. This combines solar EUV and in-situ data together with magnetic field extrapolation, large scale MHD modeling and FIP (First Ionization Potential) bias modeling to provide a global picture from the source region of the jet to its possible signatures at 1AU. Our data analysis reveals the presence of outflow areas near the jet which are within open magnetic flux regions and which present FIP bias consistent with the FIP model results. In our picture, one of these open areas is the candidate jet source. Using a back-mapping technique we identified the arrival time of this solar plasma at the ACE spacecraft. The in-situ data show signatures of changes in the plasma and magnetic field parameters, with FIP bias consistent with the possible passage of the jet material. Our results highlight the importance of remote sensing and in-situ coordinated observations as a key to solve the connectivity problem. We discuss our results in view of the recent Solar Orbiter launch which is currently providing such unique data., Comment: 53 pages, 15 figures, 5 tables, accepted for publication in Space Science Reviews

Aims. We aim to develop a fast and consistent extrapolation method to model multiple layers of the solar atmosphere. Methods. The new approach combines the magnetohydrostatic (MHS) extrapolation which models the solar low atmosphere in a flat box and the nonlinear force-free field (NLFFF) extrapolation which models the solar corona with a chromospheric vector magnetogram deduced from the MHS extrapolation. We test our code with a snapshot of a radiative magnetohydrodynamic simulation of a solar flare. Comparisons are conducted by several metrics quantitatively. Results. Based on a number of test runs, we find out the optimized configuration for the combination of two extrapolations with a 5.8-Mm-high box for the MHS extrapolation and a magnetogram at a height of 1 Mm for the NLFFF extrapolation. The new approach under this configuration is able to reconstruct the magnetic fields in multi-layers accurately and efficiently. Based on figures of merit that are used to assess the performance of different extrapolations (NLFFF extrapolation, MHS extrapolation, and the combined one), we find the combined extrapolation reaches accuracy of the MHS extrapolation which is better than the NLFFF extrapolation. The combined extrapolation is moderately efficient for application to magnetograms with high resolution., Comment: Accepted for publication in A&A

Context. Understanding the 3D magnetic field as well as the plasma in the chromosphere and transition region is important. One way is to extrapolate the magnetic field and plasma from the routinely measured vector magnetogram on the photosphere based on the assumption of the magnetohydrostatic (MHS) state. However, photospheric data may be inconsistent with the MHS assumption. Therefore, we must study the restriction on the photospheric magnetic field, which is required by the MHS system. Moreover, the data should be transformed accordingly before MHS extrapolations can be applied. Aims. We aim to obtain a set of surface integrals as criteria for the MHS system and use this set of integrals to preprocess a vector magnetogram. Methods. By applying Gauss' theorem and assuming an isolated active region on the Sun, we related the magnetic energy and forces in the volume to the surface integral on the photosphere. The same method was applied to obtain restrictions on the photospheric magnetic field as necessary criteria for a MHS system. We used an optimization method to preprocess the data to minimize the deviation from the criteria as well as the measured value. Results. By applying the virial theorem to the active region, we find the boundary integral that is used to compute the energy of a force-free field usually underestimates the magnetic energy of a large active region. We also find that the MHS assumption only requires the x-, y-component of net Lorentz force and the z-component of net torque to be zero. These zero components are part of Aly's criteria for a force-free field. However, other components of net force and torque can be non-zero values. According to new criteria, we preprocess the magnetogram to make it more consistent with the MHS system and, at the same time close, to the original data., Comment: Accepted by A&A

In this work we describe a numerical optimization method for computing stationary MHD-equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma $\beta$ and Alfv\'en Mach number $M_A$ are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where $\beta$ and $M_A$ are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magneto-static models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe., Comment: 18 pages, 6 figures, 2 tables, Solar Physics, accepted

By direct measurements of the gas temperature, the Atacama Large Millimeter/sub-millimeter Array (ALMA) has yielded a new diagnostic tool to study the solar chromosphere. Here we present an overview of the brightness-temperature fluctuations from several high-quality and high-temporal-resolution (i.e., 1 and 2 sec cadence) time series of images obtained during the first two years of solar observations with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz) and 1.25 mm (239 GHz), respectively. The various datasets represent solar regions with different levels of magnetic flux. We perform Fast Fourier and Lomb-Scargle transforms to measure both the spatial structuring of dominant frequencies and the average global frequency distributions of the oscillations (i.e., averaged over the entire field of view). We find that the observed frequencies significantly vary from one dataset to another, which is discussed in terms of the solar regions captured by the observations (i.e., linked to their underlying magnetic topology). While the presence of enhanced power within the frequency range 3-5 mHz is found for the most magnetically quiescent datasets, lower frequencies dominate when there is significant influence from strong underlying magnetic field concentrations (present inside and/or in the immediate vicinity of the observed field of view). We discuss here a number of reasons which could possibly contribute to the power suppression at around 5.5 mHz in the ALMA observations. However, it remains unclear how other chromospheric diagnostics (with an exception of Halpha line-core intensity) are unaffected by similar effects, i.e., they show very pronounced 3-min oscillations dominating the dynamics of the chromosphere, whereas only a very small fraction of all the pixels in the ten ALMA data sets analysed here show peak power near 5.5 mHz., Comment: Accepted for publication in Philosophical Transactions of the Royal Society A, 29 pages, 12 figures

We present a multiwavelength analysis of two homologous, short lived, impulsive flares of GOES class M1.4 and M7.3, that occurred from a very localized mini-sigmoid region within the active region NOAA 12673 on 2017 September 7. Both flares were associated with initial jet-like plasma ejection which for a brief amount of time moved toward east in a collimated manner before drastically changing direction toward southwest. Non-linear force-free field extrapolation reveals the presence of a compact double-decker flux rope configuration in the mini-sigmoid region prior to the flares. A set of open field lines originating near the active region which were most likely responsible for the anomalous dynamics of the erupted plasma, gave the earliest indication of an emerging coronal hole near the active region. The horizontal field distribution suggests a rapid decay of the field above the active region, implying high proneness of the flux rope system toward eruption. In view of the low coronal double-decker flux ropes and compact extreme ultra-violet (EUV) brightening beneath the filament along with associated photospheric magnetic field changes, our analysis supports the combination of initial tether-cutting reconnection and subsequent torus instability for driving the eruption., Comment: 25 pages, 11 figures, 2 tables; accepted for publication in the Astrophysical Journal

Context. High resolution magnetic field measurements are routinely done only in the solar photosphere. Higher layers like the chromosphere and corona can be modeled by extrapolating the photospheric magnetic field upward. In the solar corona, plasma forces can be neglected and the Lorentz force vanishes. This is not the case in the upper photosphere and chromosphere where magnetic and non-magnetic forces are equally important. One way to deal with this problem is to compute the plasma and magnetic field self-consistently with a magnetohydrostatic (MHS) model. Aims. We aim to derive the magnetic field, plasma pressure and density of AR11768 by applying the newly developed extrapolation technique to the SUNRISE/IMaX data. Methods. An optimization method is used for the MHS modeling. The initial conditions consist of a nonlinear force-free field (NLFFF) and a gravity-stratified atmosphere. Results. In the non-force-free layer, which is spatially resolved by the new code, Lorentz forces are effectively balanced by the gas pressure gradient force and the gravity force. The pressure and density are depleted in strong field regions, which is consistent with observations. Denser plasma, however, is also observed at some parts of the active region edges. In the chromosphere, the fibril-like plasma structures trace the magnetic field nicely. Bright points in SUNRISE/SuFI 3000 {$\AA$} images are often accompanied by the plasma pressure and electric current concentrations. In addition, the average of angle between MHS field lines and the selected chromospheric fibrils is $11.8^\circ$, which is smaller than those computed from the NLFFF model ($15.7^\circ$) and linear MHS model ($20.9^\circ$). This indicates that the MHS solution provides a better representation of the magnetic field in the chromosphere., Comment: 7 pages, 11 figures, accepted for publication in A&A

For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar atmosphere are not force-free. While some numerical extrapolation methods using magnetohydrostatic magnetic fields have been suggested, a complementary and numerically comparatively cheap method is to use analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In this paper, we present a new family of solutions for a special class of analytical three-dimensional magnetohydrostatic equilibria, which can be of use for such magnetic field extrapolation. The new solutions allow for the more flexible modelling of a transition from non-force-free to (linear) force-free magnetic fields. In particular, the height and width of the region where this transition takes place can be specified by choosing appropriate model parameters., Comment: 21 pages, 9 figures, accepted for publication in Solar Physics

Context. On the sun, the magnetic field vector is measured routinely only in the photosphere. By using these photospheric measurements as boundary condition, we developed the magnetohydrostatic (MHS) extrapolation to model the solar atmosphere. The model makes assumption about the relative importance of magnetic and non-magnetic forces. While the solar corona is force-free, this is not the case in photosphere and chromosphere. Aim. The model has been tested with an exact equilibria in \cite{zw18}. Here we present a more challenging and realistic test of our model with radiative MHD simulation of a solar flare. Methods. By using the optimization method, the MHS model computes self-consistently the magnetic field, plasma pressure and density. The nonlinear force-free field (NLFFF) and gravity stratified atmosphere along the field line are assumed as the initial condition of the optimization. Results. Compared with NLFFF, the MHS model gives an improved magnetic field not only in magnitude and direction, but also in the magnetic connectivity. Besides, the MHS model is able to recover the main structure of the plasma in the photosphere and chromosphere., Comment: Accepted for publication in Astronomy and Astrophysics

In a thorough study, we investigate the origin of a remarkable plasma and magnetic field configuration observed in situ on June 22, 2011 near L1, which appears to be a magnetic ejecta (ME) and a shock signature engulfed by a solar wind high-speed stream (HSS). We identify the signatures as an Earth-directed coronal mass ejection (CME), associated with a C7.7 flare on June 21, 2011, and its interaction with a HSS, which emanates from a coronal hole (CH) close to the launch site of the CME. The results indicate that the major interaction between the CME and the HSS starts at a height of 1.3 Rsun up to 3 Rsun. Over that distance range, the CME undergoes a strong north-eastward deflection of at least 30 degrees due to the open magnetic field configuration of the CH. We perform a comprehensive analysis for the CME-HSS event using multi-viewpoint data (from the Solar TErrestrial RElations Observatories, the Solar and Heliospheric Observatory and the Solar Dynamics Observatory), and combined modeling efforts (nonlinear force-free field modeling, Graduated Cylindrical Shell CME modeling, and the Forecasting a CMEs Altered Trajectory ForeCAT model). We aim at better understanding its early evolution and interaction process as well as its interplanetary propagation and related in situ signatures, and finally the resulting impact on the Earth's magnetosphere., Comment: Accepted in Solar Physics on August 26, 2019

Understanding the relationship between the magnetic field and coronal heating is one of the central problems of solar physics. However, studies of the magnetic properties of impulsively heated loops have been rare. We present results from a study of 34 evolving coronal loops observed in the Fe XVIII line component of AIA/SDO 94 A filter images from three active regions with different magnetic conditions. We show that the peak intensity per unit cross-section of the loops depends on their individual magnetic and geometric properties. The intensity scales proportionally to the average field strength along the loop ($B_{avg}$) and inversely with the loop length ($L$) for a combined dependence of $(B_{avg}/L)^{0.52\pm0.13}$. These loop properties are inferred from magnetic extrapolations of the photospheric HMI/SDO line-of-sight and vector magnetic field in three approximations: potential and two Non Linear Force-Free (NLFF) methods. Through hydrodynamic modeling (EBTEL model) we show that this behavior is compatible with impulsively heated loops with a volumetric heating rate that scales as $\epsilon_H\sim B_{avg}^{0.3\pm0.2}/L^{0.2\pm^{0.2}_{0.1}}$., Comment: Astrophysical Journal, in press

Modeling the interface region between solar photosphere and corona is challenging, because the relative importance of magnetic and plasma forces change by several orders of magnitude. While the solar corona can be modeled by the force-free assumption, we need to take care about plasma forces (pressure gradient and gravity) in photosphere and chromosphere, here within the magneto-hydro-static (MHS) model. We solve the MHS equations with the help of an optimization principle and use vector magnetogram as boundary condition. Positive pressure and density are ensured by replacing them with two new basic variables. The Lorentz force during optimization is used to update the plasma pressure on the bottom boundary, which makes the new extrapolation works even without pressure measurement on the photosphere. Our code is tested by using a linear MHS model as reference. From the detailed analyses, we find that the newly developed MHS extrapolation recovers the reference model at high accuracy. The MHS extrapolation is, however, numerically more expensive than the nonlinear force-free field (NLFFF) extrapolation and consequently one should limit their application to regions where plasma forces become important, e.g. in a layer of about 2 Mm above the photosphere., Comment: accepted for publication in ApJ

It is widely believed that loops observed in the solar atmosphere trace out magnetic field lines. However, the degree to which magnetic field extrapolations yield field lines that actually do follow loops has yet to be studied systematically. In this paper we apply three different extrapolation techniques - a simple potential model, a NLFF model based on photospheric vector data, and a NLFF model based on forward fitting magnetic sources with vertical currents - to 15 active regions that span a wide range of magnetic conditions. We use a distance metric to assess how well each of these models is able to match field lines to the 12,202 loops traced in coronal images. These distances are typically 1-2". We also compute the misalignment angle between each traced loop and the local magnetic field vector, and find values of 5-12$^\circ$. We find that the NLFF models generally outperform the potential extrapolation on these metrics, although the differences between the different extrapolations are relatively small. The methodology that we employ for this study suggests a number of ways that both the extrapolations and loop identification can be improved., Comment: Accepted for publication in ApJ

We report on high-resolution imaging and spectral observations of eruptions of a spiral structure in the transition region, which were taken with the Interface Region Imaging Spectrometer (IRIS), the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI). The eruption coincided with the appearance of two series of jets, with velocities comparable to the Alfv\'en speeds in their footpoints. Several pieces of evidence of magnetic braiding in the eruption are revealed, including localized bright knots, multiple well-separated jet threads, transition region explosive events and the fact that all these three are falling into the same locations within the eruptive structures. Through analysis of the extrapolated three-dimensional magnetic field in the region, we found that the eruptive spiral structure corresponded well to locations of twisted magnetic flux tubes with varying curl values along their lengths. The eruption occurred where strong parallel currents, high squashing factors, and large twist numbers were obtained. The electron number density of the eruptive structure is found to be $\sim3\times10^{12}$ cm$^{-3}$, indicating that significant amount of mass could be pumped into the corona by the jets. Following the eruption, the extrapolations revealed a set of seemingly relaxed loops, which were visible in the AIA 94 \AA\ channel indicating temperatures of around 6.3 MK. With these observations, we suggest that magnetic braiding could be part of the mechanisms explaining the formation of solar eruption and the mass and energy supplement to the corona., Comment: 11 figs, accepted for publication in ApJ

Getting insights into the 3D structure of the solar coronal magnetic field have been done in the past by two completely different approaches: (1.) Nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. (2.) Stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strength and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the computed 3D coronal magnetic field with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by the inclusion of stereoscopic constrains. The method was successfully tested with synthetic data and within this work we apply the newly developed code to a combined data-set from SDO/HMI, SDO/AIA and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that prescribing the shape of the 3D stereoscopically reconstructed loops the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field which indicates the improved quality of the force-free solution obtained by S-NLFFF., Comment: 9 pages, 7 figures

How the solar corona is heated to high temperatures remains an unsolved mystery in solar physics. In the present study we analyse observations of 50 whole active-region loops taken with the Extreme-ultraviolet Imaging Spectrometer (EIS) on board the Hinode satellite. Eleven loops were classified as cool (<1 MK) and 39 as warm (1-2 MK) loops. We study their plasma parameters such as densities, temperatures, filling factors, non-thermal velocities and Doppler velocities. We combine spectroscopic analysis with linear force-free magnetic-field extrapolation to derive the three-dimensional structure and positioning of the loops, their lengths and heights as well as the magnetic field strength along the loops. We use density-sensitive line pairs from Fe XII, Fe XIII, Si X and Mg VII ions to obtain electron densities by taking special care of intensity background-subtraction. The emission-measure loci method is used to obtain the loop temperatures. We find that the loops are nearly isothermal along the line-of-sight. Their filling factors are between 8% and 89%. We also compare the observed parameters with the theoretical RTV scaling law. We find that most of the loops are in an overpressure state relative to the RTV predictions. In a followup study, we will report a heating model of a parallel-cascade-based mechanism and will compare the model parameters with the loop plasma and structural parameters derived here., Comment: ApJ, accepted for publication

Many magnetic structures in the solar atmosphere evolve rather slowly so that they can be assumed as (quasi-)static or (quasi-)stationary and represented via magneto-hydrostatic (MHS) or stationary magneto-hydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in stationary MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the non-canonical transformation method produces quasi-3D solutions of stationary MHD by mapping 2D or 2.5D MHS equilibria to corresponding stationary MHD states, i.e., states that display the same field line structure as the original MHS equilibria. These stationary MHD states exist on magnetic flux surfaces of the original 2D MHS states. Although the flux surfaces and therefore also the equilibria have a 2D character, these stationary MHD states depend on all three coordinates and display highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provide the base for efficient dissipation of the magnetic energy in the solar corona by Ohmic heating. We also discuss the possibility of maintaining an important subset of non-linear MHS states, namely force-free fields, by stationary flows. We find that force-free fields with non-linear flows only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution., Comment: 14 pages, 5 figures, accepted to ApJ

The prediction of the arrival time for fast coronal mass ejections (CMEs) and their associated shocks is highly desirable in space weather studies. In this paper, we use two shock propagation models, i.e. Data Guided Shock Time Of Arrival (DGSTOA) and Data Guided Shock Propagation Model (DGSPM), to predict the kinematical evolution of interplanetary shocks associated with fast CMEs. DGSTOA is based on the similarity theory of shock waves in the solar wind reference frame, and DGSPM on the non-similarity theory in the stationary reference frame. The inputs are the kinematics of the CME front at the maximum speed moment obtained from the geometric triangulation method applied to STEREO imaging observations together with the Harmonic Mean approximation. The outputs provide the subsequent propagation of the associated shock. We apply these models to the CMEs on 2012 January 19, January 23, and March 7. We find that the shock models predict reasonably well the shock's propagation after the impulsive acceleration. The shock's arrival time and local propagation speed at Earth predicted by these models are consistent with in situ measurements of WIND. We also employ the Drag-Based Model (DBM) as a comparison, and find that it predicts a steeper deceleration than the shock models after the rapid deceleration phase. The predictions of DBM at 1 AU agree with the following ICME or sheath structure, not the preceding shock. These results demonstrate the applicability of the shock models used here for future arrival time prediction of interplanetary shocks associated with fast CMEs., Comment: accepted for publication in ApJS

We investigate the evolution of NOAA Active Region 11817 during 2013 August 10--12, when it developed a complex field configuration and produced four confined, followed by two eruptive, flares. These C-and-above flares are all associated with a magnetic flux rope (MFR) located along the major polarity inversion line, where shearing and converging photospheric flows are present. Aided by the nonlinear force-free field modeling, we identify the MFR through mapping magnetic connectivities and computing the twist number $\mathcal{T}_w$ for each individual field line. The MFR is moderately twisted ($|\mathcal{T}_w| < 2$) and has a well-defined boundary of high squashing factor $Q$. We found that the field line with the extremum $|\mathcal{T}_w|$ is a reliable proxy of the rope axis, and that the MFR's peak $|\mathcal{T}_w|$ temporarily increases within half an hour before each flare while it decreases after the flare peak for both confined and eruptive flares. This pre-flare increase in $|\mathcal{T}_w|$ has little effect on the active region's free magnetic energy or any other parameters derived for the whole region, due to its moderate amount and the MFR's relatively small volume, while its decrease after flares is clearly associated with the stepwise decrease in free magnetic energy due to the flare. We suggest that $\mathcal{T}_w$ may serve as a useful parameter in forewarning the onset of eruption, and therefore, the consequent space weather effects. The helical kink instability is identified as the prime candidate onset mechanism for the considered flares., Comment: submitted to ApJ

The dynamic properties of flare ribbons and the often associated filament eruptions can provide crucial information on the flaring coronal magnetic field. This Letter analyzes the GOES-class X1.0 flare on 2014 March 29 (SOL2014-03-29T17:48), in which we found an asymmetric eruption of a sigmoidal filament and an ensuing circular flare ribbon. Initially both EUV images and a preflare nonlinear force-free field model show that the filament is embedded in magnetic fields with a fan-spine-like structure. In the first phase, which is defined by a weak but still increasing X-ray emission, the western portion of the sigmoidal filament arches upward and then remains quasi-static for about five minutes. The western fan-like and the outer spine-like fields display an ascending motion, and several associated ribbons begin to brighten. Also found is a bright EUV flow that streams down along the eastern fan-like field. In the second phase that includes the main peak of hard X-ray (HXR) emission, the filament erupts, leaving behind two major HXR sources formed around its central dip portion and a circular ribbon brightened sequentially. The expanding western fan-like field interacts intensively with the outer spine-like field, as clearly seen in running difference EUV images. We discuss these observations in favor of a scenario where the asymmetric eruption of the sigmoidal filament is initiated due to an MHD instability and further facilitated by reconnection at a quasi-null in corona; the latter is in turn enhanced by the filament eruption and subsequently produces the circular flare ribbon., Comment: 7 pages, 5 figures, accepted to ApJ Letters

The geometrical shapes and the physical properties of stellar wind -- interstellar medium interaction regions form an important stage for studying stellar winds and their embedded magnetic fields as well as cosmic ray modulation. Our goal is to provide a proper representation and classification of counter-flow configurations and counter-flow interfaces in the frame of fluid theory. In addition we calculate flows and large-scale electromagnetic fields based on which the large-scale dynamics and its role as possible background for particle acceleration, e.g. in the form of anomalous cosmic rays, can be studied. We find that for the definition of the boundaries, which are determining the astropause shape, the number and location of magnetic null points and stagnation points is essential. Multiple separatrices can exist, forming a highly complex environment for the interstellar and stellar plasma. Furthermore, the formation of extended tail structures occur naturally, and their stretched field and streamlines provide surroundings and mechanisms for the acceleration of particles by field-aligned electric fields., Comment: 10 pages, 4 Figures

This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes., Comment: 109 pages, 30 Figures, to be published in A&ARv

We carry out a comprehensive investigation comparing the three-dimensional magnetic field restructuring, flare energy release, and the helioseismic response, of two homologous flares, the 2011 September 6 X2.1 (FL1) and September 7 X1.8 (FL2) flares in NOAA AR 11283. In our analysis, (1) a twisted flux rope (FR) collapses onto the surface at a speed of 1.5 km/s after a partial eruption in FL1. The FR then gradually grows to reach a higher altitude and collapses again at 3 km/s after a fuller eruption in FL2. Also, FL2 shows a larger decrease of the flux-weighted centroid separation of opposite magnetic polarities and a greater change of the horizontal field on the surface. These imply a more violent coronal implosion with corresponding more intense surface signatures in FL2. (2) The FR is inclined northward, and together with the ambient fields, it undergoes a southward turning after both events. This agrees with the asymmetric decay of the penumbra observed in the peripheral regions. (3) The amounts of free magnetic energy and nonthermal electron energy released during FL1 are comparable to those of FL2 within the uncertainties of the measurements. (4) No sunquake was detected in FL1; in contrast, FL2 produced two seismic emission sources S1 and S2 both lying in the penumbral regions. Interestingly, S1 and S2 are connected by magnetic loops, and the stronger source S2 has weaker vertical magnetic field. We discuss these results in relation to the implosion process in the low corona and the sunquake generation., Comment: 12 pages, 9 figures, accepted to the Astrophysical Journal

The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chosen for coronal magnetic field modeling on resulting model solution. We apply spherical Optimization procedure to vector magnetogram data of Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) with four Active Region observed on 09 March 2012 at 20:55UT. The results imply that quantities like magnetic flux density, electric current density and free magnetic energy density of ARs of interest are significantly different from the corresponding quantities obtained in the same region within the wider field of view. The difference is even more pronounced in the regions where there are connections to outside the domain., Comment: Submitted to Solar Physics Journal, 5 figures, 14 pages

We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The \nlfff\ extrapolation method was applied to the 12 minutes cadence data obtained with the \hmi\ (HMI) onboard the \sdo\ (SDO) during five days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including an hyperbolic flux tube (HFT) configuration which is relatively stable at the time scale of the flare ($\sim 1-2$ hours). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT which has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In final, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption., Comment: Accepted by ApJ

Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of its rapid process has been of challenge. In this Letter we present, using a nonlinear force-free field (NLFFF) extrapolation technique, a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by the analysis of the field lines traced from positions of four conspicuous flare 1700 A footpoints observed at the event onset. Right before the flare, the four footpoints are located very close to the regions of local maxima of magnetic twist index. Especially, the field lines from the inner two footpoints form two strongly twisted flux bundles (up to ~1.2 turns), which shear past each other and reach out close to the outer two footpoints, respectively. Immediately after the flare, the twist index of regions around the footpoints greatly diminish and the above field lines become low lying and less twisted (~0.6 turns), overarched by loops linking the later formed two flare ribbons. About 10% of the flux (~3x10^19 Mx) from the inner footpoints has undergone a footpoint exchange. This portion of flux originates from the edge regions of the inner footpoints that are brightened first. These rapid changes of magnetic field connectivity inferred from the NLFFF extrapolation are consistent with the tether-cutting magnetic reconnection model., Comment: 6 pages, 5 figures, accepted to the Astrophysical Journal Letters

We consider a magnetic configuration consisting of an arcade structure and a detached plasmoid, resulting from a magnetic reconnection process, as is typically found in connection with solar flares. We study spontaneous current fragmentation caused by shear and vortex plasma flows. An exact analytical transformation method was applied to calculate self-consistent solutions of the nonlinear stationary MHD equations. The assumption of incompressible field-aligned flows implies that both the Alfven Mach number and the mass density are constant on field lines. We first calculated nonlinear MHS equilibria with the help of the Liouville method, emulating the scenario of a solar eruptive flare configuration with plasmoids and flare arcade. Then a Mach number profile was constructed that describes the upflow along the open magnetic field lines and implements a vortex flow inside the plasmoid. This Mach number profile was used to map the MHS equilibrium to the stationary one. We find that current fragmentation takes place at different locations within our configuration. Steep gradients of the Alfven Mach number are required, implying the strong influence of shear flows on current amplification and filamentation of the MHS current sheets. Crescent- or ring-like structures appear along the outer separatrix, butterfly structures between the upper and lower plasmoids, and strong current peaks close the lower boundary. Impressing an intrinsic small-scale structure on the upper plasmoid results in strong fragmentation of the plasmoid. Hence fragmentation of current sheets and plasmoids is an inherent property of MHD theory. Transformations from MHS into MHD steady-states deliver fine-structures needed for plasma heating and acceleration of particles and bulk plasma flows in dissipative events that are typically connected to magnetic reconnection processes in flares and coronal mass ejections., Comment: 12 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

The moss is the area at the footpoint of the hot (3 to 5 MK) loops forming the core of the active region where emission is believed to result from the heat flux conducted down to the transition region from the hot loops. Studying the variation of Doppler shift as a function of line formation temperatures over the moss area can give clues on the heating mechanism in the hot loops in the core of the active regions. We investigate the absolute Doppler shift of lines formed at temperatures between 1 MK and 2 MK in a moss area within active region NOAA 11243 using a novel technique that allows determining the absolute Doppler shift of EUV lines by combining observations from the SUMER and EIS spectrometers. The inner (brighter and denser) part of the moss area shows roughly constant blue shift (upward motions) of 5 km/s in the temperature range of 1 MK to 1.6 MK. For hotter lines the blue shift decreases and reaches 1 km/s for Fe xv 284 {\AA} (~2 MK). The measurements are discussed in relation to models of the heating of hot loops. The results for the hot coronal lines seem to support the quasi-steady heating models for non-symmetric hot loops in the core of active regions., Comment: 11 pages, 15 Figures, Astronomy and Astrophysics (in press)

The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. 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., Comment: 49 pages, 11 figures, Living Reviews in Solar Physics, accepted

Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role for the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfven-Mach number M_A, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant M_A, vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where M_A varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2D it is possible to have current but no vortex sheets. In 2D vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfven Mach numbers into account. The current sheet can vanish if the Alfven Mach number is (almost) constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfven Mach numbers M_A<<1, but also for M_A~1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given., Comment: 10 pages, 2 figures, accepted for publication in Annales Geophysicae

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6e32 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3e32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion", and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic., Comment: Eq. (A1) corrected

The rapid, irreversible change of the photospheric magnetic field has been recognized as an important element of the solar flare process. This Letter reports such a rapid change of magnetic fields during the 2011 February 13 M6.6 flare in NOAA AR 11158 that we found from the vector magnetograms of the Helioseismic and Magnetic Imager with 12-min cadence. High-resolution magnetograms of Hinode that are available at ~-5.5, -1.5, 1.5, and 4 hrs relative to the flare maximum are used to reconstruct three-dimensional coronal magnetic field under the nonlinear force-free field (NLFFF) assumption. UV and hard X-ray images are also used to illuminate the magnetic field evolution and energy release. The rapid change is mainly detected by HMI in a compact region lying in the center of the magnetic sigmoid, where the mean horizontal field strength exhibited a significant increase by 28%. The region lies between the initial strong UV and hard X-ray sources in the chromosphere, which are cospatial with the central feet of the sigmoid according to the NLFFF model. The NLFFF model further shows that strong coronal currents are concentrated immediately above the region, and that more intriguingly, the coronal current system underwent an apparent downward collapse after the sigmoid eruption. These results are discussed in favor of both the tether-cutting reconnection producing the flare and the ensuing implosion of the coronal field resulting from the energy release., Comment: 7 pages, 5 figures, accepted to the Astrophysical Journal Letters

Polar plumes are seen as elongated objects starting at the solar polar regions. Here, we analyze these objects from a sequence of images taken simultaneously by the three spacecraft telescopes STEREO/EUVI A and B, and SOHO/EIT. We establish a method capable of automatically identifying plumes in solar EUV images close to the limb at 1.01 - 1.39 R in order to study their temporal evolution. This plume-identification method is based on a multiscale Hough-wavelet analysis. Then two methods to determined their 3D localization and structure are discussed: First, tomography using the filtered back-projection and including the differential rotation of the Sun and, secondly, conventional stereoscopic triangulation. We show that tomography and stereoscopy are complementary to study polar plumes. We also show that this systematic 2D identification and the proposed methods of 3D reconstruction are well suited, on one hand, to identify plumes individually and on the other hand, to analyze the distribution of plumes and inter-plume regions. Finally, the results are discussed focusing on the plume position with their cross-section area., Comment: 22 pages, 10 figures, Solar Physics article

Understanding the solar outer atmosphere requires concerted, simultaneous solar observations from the visible to the vacuum ultraviolet (VUV) and soft X-rays, at high spatial resolution (between 0.1" and 0.3"), at high temporal resolution (on the order of 10 s, i.e., the time scale of chromospheric dynamics), with a wide temperature coverage (0.01 MK to 20 MK, from the chromosphere to the flaring corona), and the capability of measuring magnetic fields through spectropolarimetry at visible and near-infrared wavelengths. Simultaneous spectroscopic measurements sampling the entire temperature range are particularly important. These requirements are fulfilled by the Japanese Solar-C mission (Plan B), composed of a spacecraft in a geosynchronous orbit with a payload providing a significant improvement of imaging and spectropolarimetric capabilities in the UV, visible, and near-infrared with respect to what is available today and foreseen in the near future. The Large European Module for solar Ultraviolet Research (LEMUR), described in this paper, is a large VUV telescope feeding a scientific payload of high-resolution imaging spectrographs and cameras. LEMUR consists of two major components: a VUV solar telescope with a 30 cm diameter mirror and a focal length of 3.6 m, and a focal-plane package composed of VUV spectrometers covering six carefully chosen wavelength ranges between 17 and 127 nm. The LEMUR slit covers 280" on the Sun with 0.14" per pixel sampling. In addition, LEMUR is capable of measuring mass flows velocities (line shifts) down to 2 km/s or better. LEMUR has been proposed to ESA as the European contribution to the Solar C mission., Comment: 35 pages, 14 figures. To appear on Experimental Astronomy

We investigate the fine structure of magnetic fields in the atmosphere of the quiet Sun. We use photospheric magnetic field measurements from {\sc Sunrise}/IMaX with unprecedented spatial resolution to extrapolate the photospheric magnetic field into higher layers of the solar atmosphere with the help of potential and force-free extrapolation techniques. We find that most magnetic loops which reach into the chromosphere or higher have one foot point in relatively strong magnetic field regions in the photosphere. $91%$ of the magnetic energy in the mid chromosphere (at a height of 1 Mm) is in field lines, whose stronger foot point has a strength of more than 300 G, i.e. above the equipartition field strength with convection. The loops reaching into the chromosphere and corona are also found to be asymmetric in the sense that the weaker foot point has a strength $B < 300$ G and is located in the internetwork. Such loops are expected to be strongly dynamic and have short lifetimes, as dictated by the properties of the internetwork fields., Comment: accepted for ApJL Sunrise special issue, 8 Pages, 4 Figures

Strong gradients in plasma flows play a major role in space and astrophysical plasmas. A typical situation is that a static plasma equilibrium is surrounded by a plasma flow, which can lead to strong plasma flow gradients at the separatrices between field lines with different magnetic topologies, e.g., planetary magnetospheres, helmet streamers in the solar corona, or at the boundary between the heliosphere and interstellar medium. Within this work we make a first step to understand the influence of these flows towards the occurrence of current sheets in a stationary state situation. We concentrate here on incompressible plasma flows and 2D equilibria, which allow us to find analytic solutions of the stationary magnetohydrodynamics equations (SMHD). First we solve the magnetohydrostatic (MHS) equations with the help of a Grad-Shafranov equation and then we transform these static equilibria into a stationary state with plasma flow. We are in particular interested to study SMHD-equilibria with strong plasma flow gradients perpendicular to separatrices. We find that induced thin current sheets occur naturally in such situations. The strength of the induced currents depend on the Alfv\'en Mach number and its gradient, and on the magnetic field., Comment: 10 pages, 6 figures, published in Annales Geophysicae

A magnetic channel - a series of polarity reversals separating elongated flux threads with opposite polarities - may be a manifestation of a highly non-potential magnetic configuration in active regions. To understand its formation we have carried out a detailed analysis of the magnetic channel in AR 10930 using data taken by the Solar Optical Telescope/Hinode. As a result, we found upflows (-0.5 to -1.0 km/s) and downflows (+1.5 to +2.0 km/s) inside and at both tips of the thread respectively, and a pair of strong vertical currents of opposite polarity along the channel. Moreover, our analysis of the nonlinear force-free fields constructed from the photospheric magnetic field indicates that the current density in the lower corona may have gradually increased as a result of the continuous emergence of the highly sheared flux along the channel. With these results, we suggest that the magnetic channel originates from the emergence of the twisted flux tube that has formed below the surface before the emergence., Comment: 11 figures, accepted for Astrophysical journal

Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this article, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate the three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems., Comment: Accepted to ApJ

The space mission 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., Comment: 18 pages, 5 figures

AIMS: We develop an optimization principle for computing stationary MHD equilibria. METHODS: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements. The program uses photospheric vector magnetograms and coronal EUV images as input. We tested our reconstruction code with the help of a semi-analytic MHD-equilibrium. The quality of the reconstruction was judged by comparing the exact and reconstructed solution qualitatively by magnetic field-line plots and EUV-images and quantitatively by several different numerical criteria. RESULTS: Our code is able to reconstruct the semi-analytic test equilibrium with high accuracy. The stationary MHD optimization code developed here has about the same accuracy as its predecessor, a non-linear force-free optimization code. The computing time for MHD-equilibria is, however, longer than for force-free magnetic fields. We also extended a well-known class of nonlinear force-free equilibria to the non-force-free regime for purposes of testing the code. CONCLUSIONS: We demonstrate that the code works in principle using tests with analytical equilibria, but it still needs to be applied to real data., Comment: 6 pages, 3 figures

CONTEXT: As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona. AIMS: We test the quality of a non-linear force-free coronal magnetic field extrapolation code with the help of a known analytical solution. METHODS: The non-linear force-free equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the force-free and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the computational box in Case I or only on the bottom boundary in Case II. We check the quality of the reconstruction by computing how well force-freeness and divergence-freeness are fulfilled and by comparing the numerical solution with the analytical solution. The comparison is done with magnetic field line plots and several quantitative measures, like the vector correlation, Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy. RESULTS: For Case I the reconstructed magnetic field shows good agreement with the original magnetic field topology, whereas in Case II there are considerable deviations from the exact solution. This is corroborated by the quantitative measures, which are significantly better for Case I. CONCLUSIONS: Despite the strong nonlinearity of the considered force-free equilibrium, the optimization method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly on the consistency of the input data, which is given only if the known solution is provided also at the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram., Comment: 6 pages, 2 figures, Research Note

Knowledge regarding the coronal magnetic field is important for the understanding of many phenomena, like flares and coronal mass ejections. Because of the low plasma beta in the solar corona the coronal magnetic field is often assumed to be force-free and we use photospheric vector magnetograph data to extrapolate the magnetic field into the corona with the help of a non-linear force-free optimization code. Unfortunately the measurements of the photospheric magnetic field contain inconsistencies and noise. In particular the transversal components (say Bx and By) of current vector magnetographs have their uncertainties. Furthermore the magnetic field in the photosphere is not necessary force-free and often not consistent with the assumption of a force-free field above. We develop a preprocessing procedure to drive the observed non force-free data towards suitable boundary conditions for a force-free extrapolation. As a result we get a data set which is as close as possible to the measured data and consistent with the force-free assumption., Comment: 20 pages, 5 figures