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The magnetic geometry of the solar atmosphere, combined with projection effects, makes it difficult to accurately map the propagation of ubiquitous waves in fibrillar structures. These waves are of interest due to their ability to carry energy into the chromosphere and deposit it through damping and dissipation mechanisms. To this end, the Interferometric Bidimensional Spectrometer (IBIS) at the Dunn Solar Telescope was employed to capture high resolution H$\alpha$ spectral scans of a sunspot, with the transverse oscillations of a prominent super-penumbral fibril examined in depth. The oscillations are re-projected from the helioprojective-cartesian frame to a new frame of reference oriented along the average fibril axis through non-linear force-free field extrapolations. The fibril was found to be carrying an elliptically polarised, propagating kink oscillation with a period of $430$ s and a phase velocity of $69\pm4$ km s$^{-1}$. The oscillation is damped as it propagates away from the sunspot with a damping length of approximately $9.2$ Mm, resulting in the energy flux decreasing at a rate on the order of $460$ W m$^{-2}$/Mm. The H$\alpha$ line width is examined and found to increase with distance from the sunspot; a potential sign of a temperature increase. Different linear and non-linear mechanisms are investigated for the damping of the wave energy flux, but a first-order approximation of their combined effects is insufficient to recreate the observed damping length by a factor of at least $3$. It is anticipated that the re-projection methodology demonstrated in this study will aid with future studies of transverse waves within fibrillar structures., Comment: Accepted for publication in ApJ with 17 pages and 13 figures

Extreme ultraviolet (EUV) observations of the quiet solar atmosphere reveal extended regions of weak emission compared to the ambient quiescent corona. The magnetic nature of these coronal features is not well understood. We study the magnetic properties of the weakly emitting extended regions, which we name coronal voids. In particular, we aim to understand whether these voids result from a reduced heat input into the corona or if they are associated with mainly unipolar and possibly open magnetic fields, similar to coronal holes. We defined the coronal voids via an intensity threshold of 75% of the mean quiet-Sun (QS) EUV intensity observed by the high-resolution EUV channel (HRIEUV) of the Extreme Ultraviolet Imager on Solar Orbiter. The line-of-sight magnetograms of the same solar region recorded by the High Resolution Telescope of the Polarimetric and Helioseismic Imager allowed us to compare the photospheric magnetic field beneath the coronal voids with that in other parts of the QS. The coronal voids studied here range in size from a few granules to a few supergranules and on average exhibit a reduced intensity of 67% of the mean value of the entire field of view. The magnetic flux density in the photosphere below the voids is 76% (or more) lower than in the surrounding QS. Specifically, the coronal voids show much weaker or no network structures. The detected flux imbalances fall in the range of imbalances found in QS areas of the same size. Conclusions. We conclude that coronal voids form because of locally reduced heating of the corona due to reduced magnetic flux density in the photosphere. This makes them a distinct class of (dark) structure, different from coronal holes., Comment: 10 pages, 11 figures

The photospheric magnetic field vector is continuously derived from measurements, while reconstruction of the three-dimensional (3D) coronal magnetic field requires modelling with photospheric measurements as a boundary condition. For decades the cycle variation of the magnetic field in the photosphere has been investigated. To present, there is no study to show the evolution of the coronal magnetic flux in the corona, nor the evolution of solar cycle magnetic free energy. The paper aims to analyze the temporal variation of the magnetic field and free magnetic energy in the solar corona for the solar cycle 24 and how the magnetic field behaves in the two hemispheres. We investigate if we can obtain better estimates of the magnetic field at Earth using the nonlinear force-free field (NLFFF) extrapolation method. To model the magnetic field over cycle 24 we apply the NLFFF optimization method to the synoptic vector magnetic maps derived from the observations of Heliospheric and Magnetic Imager (HMI) onboard Solar Dynamic Observatory (SDO). We found that during the solar cycle 24, the maximum of the Sun's dynamics is different from the sunspot number (SSN) maximum peak. The major contribution to the total unsigned flux is provided by the flux coming from the magnetic field structures other than sunspots (MSOS) within latitudes between -30 and +30 degrees. The magnetic flux variation during the solar cycle 24 shows a different evolution in the corona than in the photosphere. We found a correlation value of 0.8 between the derived magnetic energy from our model and the flare energy index derived from observations. On average, cycle 24 had a higher number of sunspots in the northern hemisphere (NH) but stronger flux in the southern hemisphere (SH) which could more effectively reach the higher layers of the atmosphere. The coupling between the hemispheres increases with height., Comment: 11 pages, 11 figures

Context. A proper estimate of the chromospheric magnetic fields is believed to improve modelling of both active region and coronal mass ejection evolution. Aims. We investigate the similarity between the chromospheric magnetic field inferred from observations and the field obtained from a magnetohydrostatic (MHS) extrapolation. Methods. Based Fe i 6173 {\AA} and Ca ii 8542 {\AA} observations of NOAA active region 12723, we employed the spatially-regularised weak-field approximation (WFA) to derive the vector magnetic field in the chromosphere from Ca ii, as well as non-LTE inversions of Fe i and Ca ii to infer a model atmosphere for selected regions. Milne-Eddington inversions of Fe i serve as photospheric boundary for the MHS model that delivers the three-dimensional field, gas pressure and density. Results. For the line-of-sight component, the MHS chromospheric field generally agrees with the non-LTE inversions and WFA, but tends to be weaker than those when larger in magnitude than 300 G. The observationally inferred transverse component is stronger, especially in magnetically weaker regions, yet the qualitative distribution with height is similar to the MHS results. For either field component the MHS chromospheric field lacks the fine structure derived from the inversions. Furthermore, the MHS model does not recover the magnetic imprint from a set of high fibrils connecting the main polarities. Conclusions. The MHS extrapolation and WFA provide a qualitatively similar chromospheric field, where the azimuth of the former is better aligned with Ca ii 8542 {\AA} fibrils than that of the WFA, especially outside strong-field concentrations. The amount of structure as well as the transverse field strengths are underestimated by the MHS extrapolation. This underscores the importance of considering a chromospheric magnetic field constraint in data-driven modelling of active regions., Comment: under review at A&A, abstract has been abridged

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate? (2) How do solar transients drive heliospheric variability? (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere? (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans (SOOPs), resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime., Comment: 20 pages, 1 figure, accepted by Astronomy & Astrophysics

Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models., Comment: 29 pages, 11 figures, accepted for publication in Space Science Reviews

A wide variety of phenomena such as gentle but persistent brightening, dynamic slender features (~100 km), and compact (~1'') ultraviolet (UV) bursts are associated with the heating of the solar chromosphere. High spatio-temporal resolution is required to capture the finer details of the likely magnetic reconnection-driven, rapidly evolving bursts. Such observations are also needed to reveal their similarities to large-scale flares, which are also thought to be reconnection driven, and more generally their role in chromospheric heating. Here we report observations of chromospheric heating in the form of a UV burst obtained with the balloon-borne observatory, SUNRISE. The observed burst displayed a spatial morphology similar to that of a large-scale solar flare with circular ribbon. While the co-temporal UV observations at 1.5'' spatial resolution and 24s cadence from the Solar Dynamics Observatory showed a compact brightening, the SUNRISE observations at diffraction-limited spatial resolution of 0.1'' at 7s cadence revealed a dynamic sub-structure of the burst that it is composed of extended ribbon-like features and a rapidly evolving arcade of thin (~0.1'' wide) magnetic loop-like features, similar to post-flare loops. Such a dynamic sub-structure reveals the small-scale nature of chromospheric heating in these bursts. Furthermore, based on magnetic field extrapolations, this heating event is associated with a complex fan-spine magnetic topology. Our observations strongly hint at a unified picture of magnetic heating in the solar atmosphere from some large-scale flares to small-scale bursts, all being associated with such a magnetic topology., Comment: Accepted for publication in A&A, online movie of the observations is available at https://goo.gl/RRDuX4

{We report on the first of a series of studies on coronal bright points investigating the physical mechanism that generates these phenomena.} {The aim of this paper is to understand the magnetic-field structure that hosts the bright points.} {We use longitudinal magnetograms taken by the Solar Optical Telescope with the Narrowband Filter Imager. For a single case, magnetograms from the Helioseismic and Magnetic Imager were added to the analysis. The longitudinal magnetic field component is used to derive the potential magnetic fields of the large regions around the bright points. A magneto-static field extrapolation method is tested to verify the accuracy of the potential field modelling. The three dimensional magnetic fields are investigated for the presence of magnetic null points and their influence on the local magnetic domain.} {In 9 out of 10 cases the bright point resides in areas where the coronal magnetic field contains an opposite polarity intrusion defining a magnetic null point above it. It is found that X-ray bright points reside, in these 9 cases, in a limited part of the projected fan dome area, either fully inside the dome or expanding over a limited area below which typically a dominant flux concentration resides. The 10th bright point is located in a bipolar loop system without an overlying null point.} {All bright points in coronal holes and two out of tree bright points in quiet Sun regions are seen to reside in regions containing a magnetic null point. An yet unidentified process(es) generates the BPs in specific regions of the fan-dome structure. }, Comment: 14 pages, 9 figures, 10 movies located at http://comp.astro.ku.dk/kg/BP/movies/, Accepted for publication in A&A

Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the \sunrise{} balloon-borne solar observatory in June 2013 as boundary condition for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magneto-static extrapolation approach, which has been applied earlier ({\it Paper I}) to a quiet Sun region observed with \sunrise{} I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110-130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents., Comment: Accepted for APJS, Sunrise special issue

A dense forest of slender bright fibrils near a small solar active region is seen in high-quality narrowband Ca II H images from the SuFI instrument onboard the Sunrise balloon-borne solar observatory. The orientation of these slender Ca II H fibrils (SCF) overlaps with the magnetic field configuration in the low solar chromosphere derived by magnetostatic extrapolation of the photospheric field observed with Sunrise/IMaX and SDO/HMI. In addition, many observed SCFs are qualitatively aligned with small-scale loops computed from a novel inversion approach based on best-fit numerical MHD simulation. Such loops are organized in canopy-like arches over quiet areas that differ in height depending on the field strength near their roots., Comment: 11 pages, 7 figures

We investigate the characteristics and the sources of the slow (< 450 km/s) solar wind during the four years (2006-2009) of low solar activity between Solar Cycles 23 and 24. We use a comprehensive set of in-situ observations in the near-Earth solar wind (Wind and ACE) and remove the periods when large-scale interplanetary coronal mass ejections were present. The investigated period features significant variations in the global coronal structure, including the frequent presence of low-latitude active regions in 2006-2007, long-lived low- and mid-latitude coronal holes in 2006 - mid-2008 and mostly the quiet Sun in 2009. We examine both Carrington Rotation averages of selected solar plasma, charge state and compositional parameters and distributions of these parameters related to Quiet Sun, Active Region Sun and the Coronal Hole Sun. While some of the investigated parameters (e.g., speed, the C^{+6}/C^{+4} and He/H ratio) show clear variations over our study period and with solar wind source type, some (Fe/O) exhibit very little changes. Our results highlight the difficulty in distinguishing between the slow solar wind sources based on the inspection of the solar wind conditions., Comment: 19 pages, 6 figures, 1 table, Solar Physics, in press

Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be force-free (the Lorentz-force vanishes), this is not the case in the mixed plasma $\beta$ environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken self-consistently into account and compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here we apply a linear approach, where the electric current density consists of a superposition of a field-line parallel current and a current perpendicular to the Sun's gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a non-linear model., Comment: ApJ, accepted, 6 Pages, 4 Figures

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting., Comment: Accepted to ApJ; comments/corrections to this article are welcome via e-mail, even after publication

In this paper, we report our multiwavelength observations of a partial filament eruption event in NOAA active region 11283 on 2011 September 8. A magnetic null point and the corresponding spine and separatrix surface are found in the active region. Beneath the null point, a sheared arcade supports the filament along the highly complex and fragmented polarity inversion line. After being activated, the sigmoidal filament erupted and split into two parts. The major part rose at the speeds of 90$-$150 km s$^{-1}$ before reaching the maximum apparent height of $\sim$115 Mm. Afterwards, it returned to the solar surface in a bumpy way at the speeds of 20$-$80 km s$^{-1}$. The rising and falling motions were clearly observed in the extreme-ultravoilet (EUV), UV, and H$\alpha$ wavelengths. The failed eruption of the main part was associated with an M6.7 flare with a single hard X-ray source. The runaway part of the filament, however, separated from and rotated around the major part for $\sim$1 turn at the eastern leg before escaping from the corona, probably along large-scale open magnetic field lines. The ejection of the runaway part resulted in a very faint coronal mass ejection (CME) that propagated at an apparent speed of 214 km s$^{-1}$ in the outer corona. The filament eruption also triggered transverse kink-mode oscillation of the adjacent coronal loops in the same AR. The amplitude and period of the oscillation were 1.6 Mm and 225 s. Our results are important for understanding the mechanisms of partial filament eruptions and provide new constraints to theoretical models. The multiwavelength observations also shed light on space weather prediction., Comment: 46 pages, 17 figures, 1 table, accepted for publication in ApJ

Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria. Within a physically simplified, but exact mathematical model, we study the electric currents and corresponding electric fields generated by shear flows. Starting from exact and analytically calculated magnetic potential fields, we solveid the nonlinear MHD equations self-consistently. By applying a magnetic shear flow and assuming a nonideal MHD environment, we calculated an electric field via Faraday's law. The formal solution for the electromagnetic field allowed us to compute an expression of an effective resistivity similar to the collisionless Speiser resistivity. We find that the electric field can be highly spatially structured, or in other words, filamented. The electric field component parallel to the magnetic field is the dominant component and is high where the resistivity has a maximum. The electric field is a potential field, therefore, the highest energy gain of the particles can be directly derived from the corresponding voltage. In our example of a coronal post-flare scenario we obtain electron energies of tens of keV, which are on the same order of magnitude as found observationally. This energy serves as a source for heating and acceleration of particles., Comment: 11 pages, 9 figures, accepted to Astronomy and Astrophysics

We study the quasi-static evolution of coronal magnetic fields constructed from the Non Linear Force Free Field (NLFFF) approximation aiming to understand the relation between the magnetic field topology and ribbon emission during an X1.5 flare in active region (AR) NOAA 11166. The flare with a quasi-elliptical, and two remote ribbons occurred on March 9, 2011 at 23:13UT over a positive flux region surrounded by negative flux at the center of the bipolar AR. Our analysis of the coronal magnetic structure with potential and NLFFF solutions unveiled the existence of a single magnetic null point associated with a fan-spine topology and is co-spatial with the hard X-ray source. The footpoints of the fan separatrix surface agree with the inner edge of the quasi-elliptical ribbon and the outer spine is linked to one of the remote ribbons. During the evolution, the slow footpoint motions stressed the fieldlines along the polarity inversion line and caused electric current layers in the corona around the fan separatrix surface. These current layers trigger magnetic reconnection as a consequence of dissipating currents, which are visible as cusped shape structures at lower heights. The reconnection process reorganised the magnetic field topology whose signatures are observed at the separatrices/QSL structure both in the photosphere and corona during the pre-to-post flare evolution. In agreement with previous numerical studies, our results suggest that the line-tied footpoint motions perturb the fan-spine system and cause null point reconnection, which eventually causes the flare emission at the footpoints of the fieldlines., Comment: Accepted, 2014, The Astrophysical Journal

Photospheric vector magnetograms from Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both non-linear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find that there is a weak correlation ($<60\%$) between FME and FI. FME shows slightly improved flare predictability relative to total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions., Comment: The paper was submitted to ApJ and it is accepted now

The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region corona, has been substantiated by high-resolution observations only recently. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on vector SDO/HMI magnetograms. We deliver estimates of the free magnetic energy associated to a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the active-region corona being heated by field line braiding. We were able to assess the coronal free energy appropriately by using vector field measurements and attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase of the overall twist of a flare-related flux rope which had been claimed by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within twelve minutes. Unlike another method, to which we compare our results to, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal 3D field line geometry -- to our knowledge for the first time., Comment: Accepted for publication in ApJ (8 pages, 5 figures)

Magnetic fields in the solar corona are responsible for a wide range of phenomena. However, any direct measurements of the coronal magnetic fields are very difficult due to lack of suitable spectral lines, weak magnetic fields, and high temperatures. Therefore, one extrapolates photospheric field measurements into the corona. Owing to low coronal plasma $\beta$, we can apply a force-free model in lowest order to study the slow evolution of active region (AR) magnetic fields. On applying these models to AR 11158 and compared with coronal plasma tracers, we found that (1) the approximation of potential field to coronal structures over large length scales is a reasonable one, 2) linear force-free (LFF) assumption to AR coronal fields may not be applicable model as it assumes uniform twist over the entire AR, and 3) for modeling fields at sheared, stressed locations where energy release in the form of flares are usually observed, non-linear force free fields (NLFFF) seem to provide a good approximation. The maximum available free-energy profile shows step-wise decrease that is sufficient to power an M-class flare as observed., Comment: To appear in BASI 2013, Bulletin of Astronomical Society of India

Solar eruptive phenomena, like flares and coronal mass ejections(CMEs) are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field only to the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using a nonlinear force-free field(NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three dimensional magnetic field, we calculate the three dimensional electric current density and free magnetic energy throughout the solar atmosphere for Carrington rotation 2124. We found that spatially, the low-lying, current-carrying core field demonstrates strong concentration of free energy in the AR core, from the photosphere to the lower corona; the coronal field becomes slightly more sheared in the lowest layer and it relaxes to the potential field configuration with height. The free energy density appears largely co-spatial with the electric current distribution., Comment: 8 Figures, Submitted to Solar Physics Journal

The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently there are several modelling techniques being used to calculate three-dimension of the field lines into the solar atmosphere. For the first time, synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. We solve the nonlinear force-free field equations using optimization principle in spherical geometry. The resulting three-dimensional magnetic fields are used to estimate the magnetic free energy content E_{free}=E_{nlfff}-E_{pot}, i.e., the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO. For a single Carrington rotation 2121, we find that the global NLFFF magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions., Comment: Submitted to Astronomy and Astrophysics Journal

Photospheric magnetic vector maps from two different instruments are used to model the nonlinear force-free coronal magnetic field above an active region. We use vector maps inferred from polarization measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI) and the Solar Optical Telescope Spectropolarimeter (SP) aboard Hinode. Besides basing our model calculations on HMI data, we use both, SP data of original resolution and scaled down to the resolution of HMI. This allows us to compare the model results based on data from different instruments and to investigate how a binning of high-resolution data effects the model outcome. The resulting 3D magnetic fields are compared in terms of magnetic energy content and magnetic topology. We find stronger magnetic fields in the SP data, translating into a higher total magnetic energy of the SP models. The net Lorentz forces of the HMI and SP lower boundaries verify their force-free compatibility. We find substantial differences in the absolute estimates of the magnetic field energy but similar relative estimates, e.g., the fraction of excess energy and of the flux shared by distinct areas. The location and extension of neighboring connectivity domains differs and the SP model fields tend to be higher and more vertical. Hence, conclusions about the magnetic connectivity based on force-free field models are to be drawn with caution. We find that the deviations of the model solution when based on the lower-resolution SP data are small compared to the differences of the solutions based on data from different instruments., Comment: 8 pages, 10 figures, APJ, accepted

The magnetic fields in the solar atmosphere structure the plasma, store free magnetic energy and produce a wide variety of active solar phenomena, like flare and coronal mass ejections(CMEs). The distribution and strength of magnetic fields are routinely measured in the solar surface(photosphere). Therefore, there is considerable interest in accurately modeling the 3D structure of the coronal magnetic field using photospheric vector magnetograms. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Nonlinear force-free field (NLFFF) models are thought to be viable tools for those task. Usually those models use Cartesian geometry. However, the spherical nature of the solar surface cannot be neglected when the field of view is large. In this work, we model the coronal magnetic field above multiple active regions using NLFFF extrapolation code using vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/ Vector Spectromagnetograph (VSM) as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with their respective coronal EUV-images from the Atmospheric Imaging Assembly (SDO/AIA) observed on October 11, 2011 and November 13, 2012. This study has found that the NLFFF model in spherical geometry reconstructs the magnetic configurations for several active regions which agrees with observations. During October 11, 2011 observation, there are substantial number of trans-equatorial loops carrying electric current., Comment: 3 Figures, Submitted to Astrophysics and Space Science Journal

Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to study solar eruptive phenomena, like flare and coronal mass ejections(CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field at the photosphere. Thus, substantial collection of magnetograms relate to the photospheric surface field only. Numerical modeling is carried out by applying state-of-the-art nonlinear force-free field (NLFFF) reconstruction. Cartesian nonlinear force-free field (NLFFF) codes are not well suited for larger domains, since the spherical nature of the solar surface cannot be neglected when the field of view is large. One of the most significant results of Solar Dynamic Observatory (SDO) mission to date has been repeated observations of large, almost global scale events in which large scale connection between active regions may play fundamental role. Therefore, it appears prudent to implement a NLFFF procedure in spherical geometry for use when large scale boundary data are available, such as from the Helioseismic and Magnetic Imager (HMI) on board SDO. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a NLFFF extrapolation codes in a full-disk using HMI data as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration better than the potential field model. We have concluded that much of trans-equatorial loops connecting the two solar hemispheres are current-free., Comment: 5 figures, Submitted to Solar Physics Journal

Extrapolation codes in Cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) on board solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). We use Helioseismic and Magnetic Imager and Vector Spectromagnetograph photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solve the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We compare quantities like the total magnetic energy content and free magnetic energy, the longitudinal distribution of the magnetic pressure and surface electric current density using our spherical geometry extrapolation code. The magnetic field lines obtained from nonlinear force-free extrapolation based on Helioseismic and Magnetic Imager and Vector Spectromagnetograph data have good agreement. However, the nonlinear force-free extrapolation based on Helioseismic and Magnetic Imager data have more contents of total magnetic energy, free magnetic energy, the longitudinal distribution of the magnetic pressure and surface electric current density compared to the one from Vector Spectromagnetograph data., Comment: 5 figures, Accepted by Astronomy and Astrophysics Journal

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, $20^\circ \times 20^\circ$. Additionally, We apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm., Comment: 34 pages, 8 figures, accepted for publication in ApJ

We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other., Comment: 9 pages, 5 figures

The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measurements are often due to measurement errors and finite nonmagnetic forces inconsistent as a boundary for a force-free field in the corona. In order to deal with these uncertainties, we developed two improvements: 1.) Preprocessing of the surface measurements in order to make them compatible with a force-free field 2.) The new code keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which have to be optimized for use with data from SDO/HMI. Within this work we describe the corresponding analysis method and evaluate the force-free equilibria by means of how well force-freeness and solenoidal conditions are fulfilled, the angle between magnetic field and electric current and by comparing projections of magnetic field lines with coronal images from SDO/AIA. We also compute the available free magnetic energy and discuss the potential influence of control parameters., Comment: 17 Pages, 6 Figures, Sol. Phys., accepted

Aims. We analyze coronagraph observations of a polar jet observed by the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument suite onboard the Solar TErrestrial RElations Observatory (STEREO) spacecraft. Methods. In our analysis we compare the brightness distribution of the jet in white-light coronagraph images with a dedicated kinetic particle model. We obtain a consistent estimate of the time that the jet was launched from the solar surface and an approximate initial velocity distribution in the jet source. The method also allows us to check the consistency of the kinetic model. In this first application, we consider only gravity as the dominant force on the jet particles along the magnetic field. Results. We find that the kinetic model explains the observed brightness evolution well. The derived initiation time is consistent with the jet observations by the EUVI telescope at various wavelengths. The initial particle velocity distribution is fitted by Maxwellian distributions and we find deviations of the high energy tail from the Maxwellian distributions. We estimate the jet's total electron content to have a mass between 3.2 \times 1014 and 1.8 \times 1015 g. Mapping the integrated particle number along the jet trajectory to its source region and assuming a typical source region size, we obtain an initial electron density between 8 \times 109 and 5 \times 1010 cm-3 that is characteristic for the lower corona or the upper chromosphere. The total kinetic energy of all particles in the jet source region amounts from 2.1 \times 1028 to 2.4 \times 1029 erg., Comment: A&A, in press

In this study, photospheric vector magnetograms obtained with the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS), are used as boundary conditions to model the three-dimensional nonlinear force-free (NLFF) coronal magnetic fields as a sequence of nonlinear force-free equilibria in spherical geometry. We study the coronal magnetic field structure inside active regions and its temporal evolution. We compare the magnetic field configuration obtained from NLFF extrapolation before and after flaring event in active region (AR) 11117 and its surroundings observed on 27 October 2010. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between AR 11117 and its surroundings. During the investigated time period, we estimate the change in free magnetic energy from before to after the flare to be 1.74x10^{32}erg which represents about 13.5% of nonlinear force-free magnetic energy before the flare. In this study, we find that electric currents from AR 11117 to its surroundings were disrupted after the flare., Comment: 14 pages, 14 figures, Accepted by Solar Physics Journal

Extrapolation codes for modelling the magnetic field in the corona in cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, \textit{e.g.}, a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions(ARs). We have studied the time evolution of magnetic field over the period of three days and found no major changes in topologies as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current., Comment: Solar Physics

The relation of the solar surface magnetic field with mesogranular cells is studied using high spatial (~ 100 km) and temporal (~ 30 sec) resolution data obtained with the IMaX instrument aboard SUNRISE. First, mesogranular cells are identified using Lagrange tracers (corks) based on horizontal velocity fields obtained through Local Correlation Tracking. After ~ 20 min of integration, the tracers delineate a sharp mesogranular network with lanes of width below about 280 km. The preferential location of magnetic elements in mesogranular cells is tested quantitatively. Roughly 85% of pixels with magnetic field higher than 100 G are located in the near neighborhood of mesogranular lanes. Magnetic flux is therefore concentrated in mesogranular lanes rather than intergranular ones. Secondly, magnetic field extrapolations are performed to obtain field lines anchored in the observed flux elements. This analysis, therefore, is independent of the horizontal flows determined in the first part. A probability density function (PDF) is calculated for the distribution of distances between the footpoints of individual magnetic field lines. The PDF has an exponential shape at scales between 1 and 10 Mm, with a constant characteristic decay distance, indicating the absence of preferred convection scales in the mesogranular range. Our results support the view that mesogranulation is not an intrinsic convective scale (in the sense that it is not a primary energy-injection scale of solar convection), but also give quantitative confirmation that, nevertheless, the magnetic elements are preferentially found along mesogranular lanes., Comment: Accepted for publication in ApJ Letters, 16 pages, 5 figures

Routine measurements of the solar magnetic field are mainly carried out in the photosphere. Therefore, one has to infer the field strength in the higher layers of the solar atmosphere from the measured photospheric field based on the assumption that the corona is force-free. Meanwhile, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations to these data before nonlinear force-free extrapolation codes can be applied. Extrapolation codes in cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure.We solve the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a restricted area of the Sun. We extend the functional by an additional term, which allows to incorporate measurement error and treat regions with lacking observational data. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS) to model the coronal magnetic field. We study two neighbouring magnetically connected active regions observed on May 15 2009. For vector magnetograms with variable measurement precision and randomly scattered data gaps (e.g., SOLIS/VSM) the new code yields field models which satisfy the solenoidal and force-free condition significantly better as it allows deviations between the extrapolated boundary field and observed boundary data within measurement errors. Data gaps are assigned to an infinite error. We extend this new scheme to spherical geometry and apply it for the first time to real data., Comment: Accepted on Astronomy and Astrophysics

Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. The field calculations can be improved by preprocessing the photospheric magnetograms. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006) and Fuhrmann et al. (2007). The two preprocessing methods were applied to a recently observed vector magnetogram. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields. Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing., Comment: Accepted for Astron. Astrophys

In this letter, we study in detail the evolution of the post-flare loops on 2005 January 15 that occurred between two consecutive solar eruption events, both of which generated a fast halo CME and a major flare. The post-flare loop system, formed after the first CME/flare eruption, evolved rapidly, as manifested by the unusual accelerating rise motion of the loops. Through nonlinear force-free field (NLFFF) models, we obtain the magnetic structure over the active region. It clearly shows that the flux rope below the loops also kept rising accompanied with increasing twist and length. Finally, the post-flare magnetic configuration evolved to a state that resulted in the second CME/flare eruption. This is an event in which the post-flare loops can re-flare in a short period of $\sim$16 hr following the first CME/flare eruption. The observed re-flaring at the same location is likely driven by the rapid evolution of the flux rope caused by the magnetic flux emergence and the rotation of the sunspot. This observation provides valuable information on CME/flare models and their prediction., Comment: 11 pages, 4 figures, 1 table, accepted for publication in ApJ Letter

Context: Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can suffer from significant uncertainties. Aims: Here we study how inaccuracies introduced into the maps of the photospheric magnetic vector from the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, which have been produced by the inversion of Stokes profiles, computed froma 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations starting directly from the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is done qualitatively by visual inspection of the magnetic field distribution and quantitatively by different metrics. Results: The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the non-linear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments. Conclusions heading: Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots., Comment: A&A, accepted, 9 Pages, 4 Figures

Context: Knowledge about the coronal magnetic field is important to the understanding the structure of the solar corona. We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. Aims: Here we develop a method for nonlinear force-free coronal magnetic field medelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure. Methods: We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates over a restricted area of the Sun. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. We develop a preprocessing procedure in spherical geometry to drive the observed non-force-free data towards suitable boundary conditions for a force-free extrapolation. Results: We test the code with the help of a semi-analytic solution and assess the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics for different boundary conditions. The reconstructed fields from the lower boundary data with the weighting function are in good agreement with the original reference fields. We added artificial noise to the boundary conditions and tested the code with and without preprocessing. The preprocessing recovered all main structures of the magnetogram and removed small-scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram with and without preprocessing. The preprocessing was found to significantly improve the agreement between the extrapolated and the exact field., Comment: 12 pages, 5 figures

Observations from the two STEREO-spacecraft give us for the first time the possibility to use stereoscopic methods to reconstruct the 3D solar corona. Classical stereoscopy works best for solid objects with clear edges. Consequently an application of classical stereoscopic methods to the faint structures visible in the optically thin coronal plasma is by no means straight forward and several problems have to be treated adequately: 1.)First there is the problem of identifying one dimensional structures -e.g. active region coronal loops or polar plumes- from the two individual EUV-images observed with STEREO/EUVI. 2.) As a next step one has the association problem to find corresponding structures in both images. 3.) Within the reconstruction problem stereoscopic methods are used to compute the 3D-geometry of the identified structures. Without any prior assumptions, e.g., regarding the footpoints of coronal loops, the reconstruction problem has not one unique solution. 4.) One has to estimate the reconstruction error or accuracy of the reconstructed 3D-structure, which depends on the accuracy of the identified structures in 2D, the separation angle between the spacecraft, but also on the location, e.g., for east-west directed coronal loops the reconstruction error is highest close to the loop top. 5.) Eventually we are not only interested in the 3D-geometry of loops or plumes, but also in physical parameters like density, temperature, plasma flow, magnetic field strength etc. Helpful for treating some of these problems are coronal magnetic field models extrapolated from photospheric measurements, because observed EUV-loops outline the magnetic field. This feature has been used for a new method dubbed 'magnetic stereoscopy'. As examples we show recent application to active region loops., Comment: 12 Pages, 9 Figures, a Review article

We present stereoscopic reconstructions of the location and inclination of polar plumes of two data sets based on the two simultaneously recorded images taken by the EUVI telescopes in the SECCHI instrument package onboard the \emph{STEREO (Solar TErrestrial RElations Observatory)} spacecraft. The ten plumes investigated show a superradial expansion in the coronal hole in 3D which is consistent with the 2D results. Their deviations from the local meridian planes are rather small with an average of $6.47^{\circ}$. By comparing the reconstructed plumes with a dipole field with its axis along the solar rotation axis, it is found that plumes are inclined more horizontally than the dipole field. The lower the latitude is, the larger is the deviation from the dipole field. The relationship between plumes and bright points has been investigated and they are not always associated. For the first data set, based on the 3D height of plumes and the electron density derived from SUMER/\emph{SOHO} Si {\sc viii} line pair, we found that electron densities along the plumes decrease with height above the solar surface. The temperature obtained from the density scale height is 1.6 to 1.8 times larger than the temperature obtained from Mg {\sc ix} line ratios. We attribute this discrepancy to a deviation of the electron and the ion temperatures. Finally, we have found that the outflow speeds studied in the O {\sc vi} line in the plumes corrected by the angle between the line of sight and the plume orientation are quite small with a maximum of 10 $\mathrm{km s^{-1}}$. It is unlikely that plumes are a dominant contributor to the fast solar wind., Comment: 25 pages, 13 figures

We aim at studying the small-scale evolution at the boundaries of an equatorial coronal hole connected with a channel of open magnetic flux with the polar region and an `isolated' one in the extreme-ultraviolet spectral range. We intend to determine the spatial and temporal scale of these changes. Imager data from TRACE in the Fe IX/X 171 A passband and EIT on-board Solar and Heliospheric Observatory in the Fe XII 195 A passband were analysed. We found that small-scale loops known as bright points play an essential role in coronal holes boundaries evolution at small scales. Their emergence and disappearance continuously expand or contract coronal holes. The changes appear to be random on a time scale comparable with the lifetime of the loops seen at these temperatures. No signature was found for a major energy release during the evolution of the loops. Although coronal holes seem to maintain their general shape during a few solar rotations, a closer look at their day-by-day and even hour-by-hour evolution demonstrates a significant dynamics. The small-scale loops (10" - 40" and smaller) which are abundant along coronal hole boundaries have a contribution to the small-scale evolution of coronal holes. Continuous magnetic reconnection of the open magnetic field lines of the coronal hole and the closed field lines of the loops in the quiet Sun is more likely to take place., Comment: 7 pages, 6 figures. in press in A&A

We study the correlation heights, which indicate the formation height of Extreme Ultraviolet (EUV) lines in an active region using observations from the EUV Imaging Spectrometer (EIS) and Solar Optical Telescope (SOT) on board \emph{Hinode}. The nonlinear force-free field (NLFFF) optimization method is adopted to extrapolate the 3D magnetic fields to higher layers. Three subregions with different characteristics are selected in the active region for this study. The results show that the formation heights in different subregions vary with their different magnetic fields or velocity patterns. After solving the line blending problem between the He {\sc \romannumeral 2} 256.32 \AA and Si {\sc \romannumeral 10} 256.37 \AA lines by the double Gaussian curve fitting, we find that the transition region lies higher in a strong magnetic area. In a pre-flare heating area there possibly exist multithermal loops as implied by comparing the Doppler velocity and the magnetic field on the solar disk., Comment: 17 pages, 5 figures, 1 table, accepted for publication in ApJ

The super-storm of November 20, 2003 was associated with a high speed coronal mass ejection which originated in the NOAA AR 10501 on November 18. This coronal mass ejection had severe terrestrial consequences leading to a geomagnetic storm with DST index of -472 nT, the strongest of the current solar cycle. In this paper, we attempt to understand the factors that led to the coronal mass ejection on November 18. We have also studied the evolution of the photospheric magnetic field of NOAA AR 10501, the source region of this coronal mass ejection. For this purpose, the MDI line-of-sight magnetograms and vector magnetograms from Solar Flare Telescope, Mitaka, obtained during November, 17-19, 2003 were analysed. In particular, quantitative estimates of the temporal variation in magnetic flux, energy and magnetic field gradient were estimated for the source active region. The evolution of these quantities was studied for the 3-day period with an objective to understand the pre-flare configuration leading up to the moderate flare which was associated with the geo-effective coronal mass ejection. We also examined the chromospheric images recorded in H-alpha from Udaipur Solar Observatory to compare the flare location with regions of different magnetic field and energy. Our observations provide evidence that the flare associated with the CME occurred at a location marked by high magnetic field gradient which led to release of free energy stored in the active region., Comment: 18 pages, 7 figures

We study the coronal magnetic field structure inside active regions and its temporal evolution. We attempt to compare the magnetic configuration of an active region in a very quiet period with that for the same region during a flare. Probably for the first time, we use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS) to model the coronal magnetic field as a sequence of nonlinear force-free equilibria. We study the active region NOAA 10960 observed on 2007 June 7 with three snapshots taken during a small C1.0 flare of time cadence 10 minutes and six snapshots during a quiet period. The total magnetic energy in the active region was approximately $3 \times 10^{25}$ J. Before the flare the free magnetic energy was about 5% of the potential field energy. A part of this excess energy was released during the flare, producing almost a potential configuration at the beginning of the quiet period. During the investigated period, the coronal magnetic energy was only a few percent higher than that of the potential field and consequently only a small C1.0 flare occurred. This was compared with an earlier investigated active region 10540, where the free magnetic energy was about 60% higher than that of the potential field producing two M-class flares. However, the free magnetic energy accumulates before and is released during the flare which appears to be the case for both large and small flares., Comment: 4 pages, 4 figures, A&A letters, accepted

We present the first reconstruction of the three-dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images. The images were taken by the two EUVI telescopes of the SECCHI instrument onboard the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12 degrees. We demostrate that these data allow to obtain a reliable three-dimensional reconstruction of sufficiently bright loops. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by SOHO/MDI. We attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force-free field model used for the extrapolation., Comment: 6 pages, 5 figures

We undertake a first attempt towards a consistent reconstruction of the coronal magnetic field and the coronal density structure. We consider a stationary solar corona which has to obey the equations of magnetohydrostatics. We solve these equations with help of a newly developed optimization scheme. As a first step we illustrate how tomographic information can be included into the reconstruction of coronal magnetic fields. In a second step we use coronal magnetic field information to improve the tomographic inversion process. As input the scheme requires magnetic field measurements on the photosphere from vector-magnetographs and the line-of-sight integrated density distribution from coronagraphs. We test our codes with well known analytic magnetohydrostatic equilibria and models. The program is planed for use within the STEREO mission., Comment: 29 pages, 6 figures

We developed a code for the reconstruction of nonlinear force-free and non-force-free coronal magnetic fields. The 3D magnetic field is computed numerically with the help of an optimization principle. The force-free and non-force-free codes are compiled in one program. The force-free approach needs photospheric vector magnetograms as input. The non-force-free code additionally requires the line-of-sight integrated coronal density distribution in combination with a tomographic inversion code. Previously the optimization approach has been used to compute magnetic fields using all six boundaries of a computational box. Here we extend this method and show how the coronal magnetic field can be reconstructed only from the bottom boundary, where the boundary conditions are measured with vector magnetographs. The program is planed for use within the Stereo mission., Comment: 23 pages, 5 figures

Coronal holes (CH) emit significantly less at coronal temperatures than quiet-Sun regions (QS), but can hardly be distinguished in most chromospheric and lower transition region lines. A key quantity for the understanding of this phenomenon is the magnetic field. We use data from SOHO/MDI to reconstruct the magnetic field in coronal holes and the quiet Sun with the help of a potential magnetic model. Starting from a regular grid on the solar surface we then trace field lines, which provide the overall geometry of the 3D magnetic field structure. We distinguish between open and closed field lines, with the closed field lines being assumed to represent magnetic loops. We then try to compute some properties of coronal loops. The loops in the coronal holes (CH) are found to be on average flatter than in the QS. High and long closed loops are extremely rare, whereas short and low-lying loops are almost as abundant in coronal holes as in the quiet Sun. When interpreted in the light of loop scaling laws this result suggests an explanation for the relatively strong chromospheric and transition region emission (many low-lying, short loops), but the weak coronal emission (few high and long loops) in coronal holes. In spite of this contrast our calculations also suggest that a significant fraction of the cool emission in CHs comes from the open flux regions. Despite these insights provided by the magnetic field line statistics further work is needed to obtain a definite answer to the question if loop statistics explain the differences between coronal holes and the quiet Sun., Comment: 26 pages, 11 figures

We compare the small-scale features visible in the Ne viii Doppler-shift map of an equatorial coronal hole (CH) as observed by SUMER with the small-scale structures of the magnetic field as constructed from a simultaneous photospheric magnetogram by a potential magnetic-field extrapolation. The combined data set is analysed with respect to the small-scale flows of coronal matter, which means that the Ne viii Doppler-shift used as tracer of the plasma flow is investigated in close connection with the ambient magnetic field. Some small closed-field regions in this largely open CH are also found in the coronal volume considered. The Doppler-shift patterns are found to be clearly linked with the field topology., Comment: 4 pages, 3 figures