Author name code: valori ADS astronomy entries on 2022-09-14 author:Valori, Gherardo ------------------------------------------------------------------------ Title: The on-ground data reduction and calibration pipeline for SO/PHI-HRT Authors: Sinjan, J.; Calchetti, D.; Hirzberger, J.; Orozco Suárez, D.; Albert, K.; Albelo Jorge, N.; Appourchaux, T.; Alvarez-Herrero, A.; Blanco Rodríguez, J.; Gandorfer, A.; Germerott, D.; Guerrero, L.; Gutierrez Marquez, P.; Kahil, F.; Kolleck, M.; Solanki, S. K.; del Toro Iniesta, J. C.; Volkmer, R.; Woch, J.; Fiethe, B.; Gómez Cama, J. M.; Pérez-Grande, I.; Sanchis Kilders, E.; Balaguer Jiménez, M.; Bellot Rubio, L. R.; Carmona, M.; Deutsch, W.; Fernandez-Rico, G.; Fernández-Medina, A.; García Parejo, P.; Gasent Blesa, J. L.; Gizon, L.; Grauf, B.; Heerlein, K.; Korpi-Lagg, A.; Lange, T.; López Jiménez, A.; Maue, T.; Meller, R.; Michalik, H.; Moreno Vacas, A.; Müller, R.; Nakai, E.; Schmidt, W.; Schou, J.; Schühle, U.; Staub, J.; Strecker, H.; Torralbo, I.; Valori, G. Bibcode: 2022arXiv220814904S Altcode: The ESA/NASA Solar Orbiter space mission has been successfully launched in February 2020. Onboard is the Polarimetric and Helioseismic Imager (SO/PHI), which has two telescopes, a High Resolution Telescope (HRT) and the Full Disc Telescope (FDT). The instrument is designed to infer the photospheric magnetic field and line-of-sight velocity through differential imaging of the polarised light emitted by the Sun. It calculates the full Stokes vector at 6 wavelength positions at the Fe I 617.3 nm absorption line. Due to telemetry constraints, the instrument nominally processes these Stokes profiles onboard, however when telemetry is available, the raw images are downlinked and reduced on ground. Here the architecture of the on-ground pipeline for HRT is presented, which also offers additional corrections not currently available on board the instrument. The pipeline can reduce raw images to the full Stokes vector with a polarimetric sensitivity of $10^{-3}\cdot I_{c}$ or better. Title: Investigating of the nature of magnetic oscillations associated with FIP effect Authors: Murabito, Mariarita; Jafarzadeh, Shahin; Van Driel-Gesztelyi, Lidia; Ermolli, Ilaria; Baker, Deborah; Brooks, David; Long, David; Jess, David; Valori, Gherardo; Stangalini, Marco Bibcode: 2022cosp...44.2591M Altcode: Observations of the photosphere, chromosphere, and corona combined with magnetic field modeling of one of the biggest sunspots of the 24 solar cycle, revealed that regions of high FIP bias plasma in the corona were magnetically linked to the locations of the intrinsic magnetic oscillations in the solar chromosphere. In order to characterize the driver of the oscillations, we analyzed the relation between the spatial distribution of the magnetic wave power and the overall field geometry and plasma parameters obtained from the multi-height spectropolarimetric non-local thermodynamic equilibrium (NLTE) inversions. In correspondence with the locations where the magnetic wave energy is observed at chromospheric heights, we found evidence in support of locally excited acoustic waves that, after crossing the equipartition layer located close to the umbra-penumbra boundary at photospheric heights, are converted into magnetic-like waves. These results indicate a direct connection between sunspot chromospheric activity and observable changes in coronal plasma composition, demonstrating the power of high resolution, multi-height studies of the solar atmosphere that will become the gold standard in the era of DKIST. Title: Understanding the Correlation between Solar Coronal Abundances and F10.7 Radio Emission Authors: To, Andy S. H.; Baker, Deborah; Long, David; James, Alexander; Brooks, David; van Driel-Gesztelyi, Lidia; Valori, Gherardo; Bastian, Tim; Lomuscio, Samantha; Stansby, David Bibcode: 2022cosp...44.2592T Altcode: Solar corona plasma composition, derived from full-Sun spectra, and the F10.7 radio flux (2.8 GHz) have been shown to be highly correlated (r = 0.88) during the recent weak solar cycle. However, this correlation becomes nonlinear at times of increased solar magnetic activity. We used co-temporal, high spatial resolution, radio (JVLA), and EUV (Hinode/EIS) images of the Sun taken on the 3 and 7 April 2020 to understand the underlying causes of the non-linearity of the FIP bias-F10.7 solar index correlation. We then calculated differential emission measures from AIA images, and paired them with the observed FIP bias to predict the bremsstrahlung component of F10.7 radio emission. Results of this study provide constraints on the amplitude of composition variability related to solar cycle amplitude, and provide an alternative method to calculate coronal composition. Title: Evolution of Plasma Composition in an Eruptive Flux Rope Authors: Baker, Deborah; Demoulin, Pascal; Long, David; Janvier, Miho; Green, Lucie; Brooks, David; van Driel-Gesztelyi, Lidia; Mihailescu, Teodora; To, Andy S. H.; Yardley, Stephanie; Valori, Gherardo Bibcode: 2022cosp...44.1361B Altcode: Magnetic flux ropes are bundles of twisted magnetic field enveloping a central axis. They harbor free magnetic energy and can be progenitors of coronal mass ejections (CMEs). However, identifying flux ropes on the Sun can be challenging. One of the key coronal observables that has been shown to indicate the presence of a flux rope is a peculiar bright coronal structure called a sigmoid. In this work, we show Hinode EUV Imaging Spectrometer observations of sigmoidal active region (AR) 10977. We analyze the coronal plasma composition in the AR and its evolution as a sigmoid (flux rope) forms and erupts as a CME. Plasma with photospheric composition was observed in coronal loops close to the main polarity inversion line during episodes of significant flux cancellation, suggestive of the injection of photospheric plasma into these loops driven by photospheric flux cancellation. Concurrently, the increasingly sheared core field contained plasma with coronal composition. As flux cancellation decreased and a sigmoid/flux rope formed, the plasma evolved to an intermediate composition in between photospheric and typical AR coronal compositions. Finally, the flux rope contained predominantly photospheric plasma during and after a failed eruption preceding the CME. Hence, plasma composition observations of AR 10977 strongly support models of flux rope formation by photospheric flux cancellation forcing magnetic reconnection first at the photospheric level then at the coronal level. Title: The identification of magnetic perturbations in the solar atmosphere Authors: Stangalini, Marco; Jafarzadeh, Shahin; Baker, Deborah; Jess, David; Murabito, Mariarita; Valori, Gherardo Bibcode: 2022cosp...44.2590S Altcode: Magneto-hydrodynamic (MHD) waves and, in particular, magnetic perturbations associated with specific wave modes are thought to be important mechanisms not only for the heating of the outer layers of the Sun's atmosphere, but also for the elemental abundance anomaly observed in the corona. High resolution spectropolarimetry is nowadays progressively extending to the upper layers of the solar atmosphere, and this provides invaluable insight into MHD wave processes up to chromospheric heights. However, the identification of real magnetic perturbations remains a difficult task due to a number of spurious effects that can mimic the signals associated with them. In this contribution we will show a novel approach to the identification of real magnetic oscillations potentially linked to FIP and discuss proxies to be used in statistical analyses. Title: The magnetic drivers of campfires seen by the Polarimetric and Helioseismic Imager (PHI) on Solar Orbiter Authors: Kahil, F.; Hirzberger, J.; Solanki, S. K.; Chitta, L. P.; Peter, H.; Auchère, F.; Sinjan, J.; Orozco Suárez, D.; Albert, K.; Albelo Jorge, N.; Appourchaux, T.; Alvarez-Herrero, A.; Blanco Rodríguez, J.; Gandorfer, A.; Germerott, D.; Guerrero, L.; Gutiérrez Márquez, P.; Kolleck, M.; del Toro Iniesta, J. C.; Volkmer, R.; Woch, J.; Fiethe, B.; Gómez Cama, J. M.; Pérez-Grande, I.; Sanchis Kilders, E.; Balaguer Jiménez, M.; Bellot Rubio, L. R.; Calchetti, D.; Carmona, M.; Deutsch, W.; Fernández-Rico, G.; Fernández-Medina, A.; García Parejo, P.; Gasent-Blesa, J. L.; Gizon, L.; Grauf, B.; Heerlein, K.; Lagg, A.; Lange, T.; López Jiménez, A.; Maue, T.; Meller, R.; Michalik, H.; Moreno Vacas, A.; Müller, R.; Nakai, E.; Schmidt, W.; Schou, J.; Schühle, U.; Staub, J.; Strecker, H.; Torralbo, I.; Valori, G.; Aznar Cuadrado, R.; Teriaca, L.; Berghmans, D.; Verbeeck, C.; Kraaikamp, E.; Gissot, S. Bibcode: 2022A&A...660A.143K Altcode: 2022arXiv220213859K Context. The Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO) spacecraft observed small extreme ultraviolet (EUV) bursts, termed campfires, that have been proposed to be brightenings near the apexes of low-lying loops in the quiet-Sun atmosphere. The underlying magnetic processes driving these campfires are not understood.
Aims: During the cruise phase of SO and at a distance of 0.523 AU from the Sun, the Polarimetric and Helioseismic Imager on Solar Orbiter (SO/PHI) observed a quiet-Sun region jointly with SO/EUI, offering the possibility to investigate the surface magnetic field dynamics underlying campfires at a spatial resolution of about 380 km.
Methods: We used co-spatial and co-temporal data of the quiet-Sun network at disc centre acquired with the High Resolution Imager of SO/EUI at 17.4 nm (HRIEUV, cadence 2 s) and the High Resolution Telescope of SO/PHI at 617.3 nm (HRT, cadence 2.5 min). Campfires that are within the SO/PHI−SO/EUI common field of view were isolated and categorised according to the underlying magnetic activity.
Results: In 71% of the 38 isolated events, campfires are confined between bipolar magnetic features, which seem to exhibit signatures of magnetic flux cancellation. The flux cancellation occurs either between the two main footpoints, or between one of the footpoints of the loop housing the campfire and a nearby opposite polarity patch. In one particularly clear-cut case, we detected the emergence of a small-scale magnetic loop in the internetwork followed soon afterwards by a campfire brightening adjacent to the location of the linear polarisation signal in the photosphere, that is to say near where the apex of the emerging loop lays. The rest of the events were observed over small scattered magnetic features, which could not be identified as magnetic footpoints of the campfire hosting loops.
Conclusions: The majority of campfires could be driven by magnetic reconnection triggered at the footpoints, similar to the physical processes occurring in the burst-like EUV events discussed in the literature. About a quarter of all analysed campfires, however, are not associated to such magnetic activity in the photosphere, which implies that other heating mechanisms are energising these small-scale EUV brightenings. Title: Evolution of Plasma Composition in an Eruptive Flux Rope Authors: Baker, D.; Green, L. M.; Brooks, D. H.; Démoulin, P.; van Driel-Gesztelyi, L.; Mihailescu, T.; To, A. S. H.; Long, D. M.; Yardley, S. L.; Janvier, M.; Valori, G. Bibcode: 2022ApJ...924...17B Altcode: 2021arXiv211011714B Magnetic flux ropes are bundles of twisted magnetic field enveloping a central axis. They harbor free magnetic energy and can be progenitors of coronal mass ejections (CMEs). However, identifying flux ropes on the Sun can be challenging. One of the key coronal observables that has been shown to indicate the presence of a flux rope is a peculiar bright coronal structure called a sigmoid. In this work, we show Hinode EUV Imaging Spectrometer observations of sigmoidal active region (AR) 10977. We analyze the coronal plasma composition in the AR and its evolution as a sigmoid (flux rope) forms and erupts as a CME. Plasma with photospheric composition was observed in coronal loops close to the main polarity inversion line during episodes of significant flux cancellation, suggestive of the injection of photospheric plasma into these loops driven by photospheric flux cancellation. Concurrently, the increasingly sheared core field contained plasma with coronal composition. As flux cancellation decreased and a sigmoid/flux rope formed, the plasma evolved to an intermediate composition in between photospheric and typical AR coronal compositions. Finally, the flux rope contained predominantly photospheric plasma during and after a failed eruption preceding the CME. Hence, plasma composition observations of AR 10977 strongly support models of flux rope formation by photospheric flux cancellation forcing magnetic reconnection first at the photospheric level then at the coronal level. Title: Disambiguation of Vector Magnetograms by Stereoscopic Observations from the Solar Orbiter (SO)/Polarimetric and Helioseismic Imager (PHI) and the Solar Dynamic Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) Authors: Valori, Gherardo; Löschl, Philipp; Stansby, David; Pariat, Etienne; Hirzberger, Johann; Chen, Feng Bibcode: 2022SoPh..297...12V Altcode: 2021arXiv211210650V Spectropolarimetric reconstructions of the photospheric vector magnetic field are intrinsically limited by the 180 ambiguity in the orientation of the transverse component. The successful launch and operation of Solar Orbiter have made the removal of the 180 ambiguity possible using solely observations obtained from two different vantage points. While the exploitation of such a possibility is straightforward in principle, it is less so in practice, and it is therefore important to assess the accuracy and limitations as a function of both the spacecrafts' orbits and measurement principles. In this work, we present a stereoscopic disambiguation method (SDM) and discuss thorough testing of its accuracy in applications to modeled active regions and quiet-Sun observations. In the first series of tests, we employ magnetograms extracted from three different numerical simulations as test fields and model observations of the magnetograms from different angles and distances. In these more idealized tests, SDM is proven to reach a 100% disambiguation accuracy when applied to moderately-to-well resolved fields. In such favorable conditions, the accuracy is almost independent of the relative position of the spacecraft with the obvious exceptions of configurations where the spacecraft are within a few degrees of co-alignment or quadrature. Even in the case of disambiguation of quiet-Sun magnetograms with significant under-resolved spatial scales, SDM provides an accuracy between 82% and 98%, depending on the field strength. The accuracy of SDM is found to be mostly sensitive to the variable spatial resolution of Solar Orbiter in its highly elliptic orbit, as well as to the intrinsic spatial scale of the observed field. Additionally, we provide an example of the expected accuracy as a function of time that can be used to optimally place remote-sensing observing windows during Solar Orbiter observation planning. Finally, as a more realistic test, we consider magnetograms that are obtained using a radiative-transfer inversion code and the SO/PHI Software siMulator (SOPHISM) applied to a 3D-simulation of a pore, and we present a preliminary discussion of the effect of the viewing angle on the observed field. In this more realistic test of the application of SDM, the method is able to successfully remove the ambiguity in strong-field areas. Title: Investigating the origin of magnetic perturbations associated with the FIP Effect Authors: Murabito, M.; Stangalini, M.; Baker, D.; Valori, G.; Jess, D. B.; Jafarzadeh, S.; Brooks, D. H.; Ermolli, I.; Giorgi, F.; Grant, S. D. T.; Long, D. M.; van Driel-Gesztelyi, L. Bibcode: 2021A&A...656A..87M Altcode: 2021arXiv210811164M Recently, magnetic oscillations were detected in the chromosphere of a large sunspot and found to be linked to the coronal locations where a first ionization potential (FIP) effect was observed. In an attempt to shed light on the possible excitation mechanisms of these localized waves, we further investigate the same data by focusing on the relation between the spatial distribution of the magnetic wave power and the overall field geometry and plasma parameters obtained from multi-height spectropolarimetric non-local thermodynamic equilibrium (NLTE) inversions of IBIS data. We find, in correspondence with the locations where the magnetic wave energy is observed at chromospheric heights, that the magnetic fields have smaller scale heights, meaning faster expansions of the field lines, which ultimately results in stronger vertical density stratification and wave steepening. In addition, the acoustic spectrum of the oscillations at the locations where magnetic perturbations are observed is broader than that observed at other locations, which suggests an additional forcing driver to the p-modes. Analysis of the photospheric oscillations in the sunspot surroundings also reveals a broader spectrum between the two opposite polarities of the active region (the leading spot and the trailing opposite polarity plage), and on the same side where magnetic perturbations are observed in the umbra. We suggest that strong photospheric perturbations between the two polarities are responsible for this broader spectrum of oscillations, with respect to the p-mode spectrum, resulting in locally excited acoustic waves that, after crossing the equipartition layer, located close to the umbra-penumbra boundary at photopheric heights, are converted into magnetic waves and steepen due to the strong density gradient.

Movie associated to Fig. 1 is available at https://www.aanda.org Title: Localized Acceleration of Energetic Particles by a Weak Shock in the Solar Corona Authors: Long, David M.; Reid, Hamish A. S.; Valori, Gherardo; O'Kane, Jennifer Bibcode: 2021ApJ...921...61L Altcode: 2021arXiv210805068L Globally propagating shocks in the solar corona have long been studied to quantify their involvement in the acceleration of energetic particles. However, this work has tended to focus on large events associated with strong solar flares and fast coronal mass ejections (CMEs), where the waves are sufficiently fast to easily accelerate particles to high energies. Here we present observations of particle acceleration associated with a global wave event which occurred on 2011 October 1. Using differential emission measure analysis, the global shock wave was found to be incredibly weak, with an Alfvén Mach number of ~1.008-1.013. Despite this, spatially resolved type III radio emission was observed by the Nançay RadioHeliograph at distinct locations near the shock front, suggesting localized acceleration of energetic electrons. Further investigation using magnetic field extrapolation identified a fan structure beneath a magnetic null located above the source active region, with the erupting CME contained within this topological feature. We propose that a reconfiguration of the coronal magnetic field driven by the erupting CME enabled the weak shock to accelerate particles along field lines initially contained within the fan and subsequently opening into the heliosphere, producing the observed type III emission. These results suggest that even weak global shocks in the solar corona can accelerate energetic particles via reconfiguration of the surrounding magnetic field. Title: Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. IV. Application to Solar Observations Authors: Thalmann, J. K.; Georgoulis, M. K.; Liu, Y.; Pariat, E.; Valori, G.; Anfinogentov, S.; Chen, F.; Guo, Y.; Moraitis, K.; Yang, S.; Mastrano, Alpha; ISSI Team on Magnetic Helicity Bibcode: 2021ApJ...922...41T Altcode: 2021arXiv210808525T In this ISSI-supported series of studies on magnetic helicity in the Sun, we systematically implement different magnetic helicity calculation methods on high-quality solar magnetogram observations. We apply finite-volume, discrete flux tube (in particular, connectivity-based) and flux-integration methods to data from Hinode's Solar Optical Telescope. The target is NOAA Active Region 10930 during a 1.5-day interval in 2006 December that included a major eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based methods yield instantaneous budgets of the coronal magnetic helicity, while the flux-integration methods allow an estimate of the accumulated helicity injected through the photosphere. The objectives of our work are twofold: a cross-validation of methods, as well as an interpretation of the complex events leading to the eruption. To the first objective, we find (i) strong agreement among the finite-volume methods, (ii) a moderate agreement between the connectivity-based and finite-volume methods, (iii) an excellent agreement between the flux-integration methods, and (iv) an overall agreement between finite-volume- and flux-integration-based estimates regarding the predominant sign and magnitude of the helicity. To the second objective, we are confident that the photospheric helicity flux significantly contributed to the coronal helicity budget and that a right-handed structure erupted from a predominantly left-handed corona during the X-class flare. Overall, we find that the use of different methods to estimate the (accumulated) coronal helicity may be necessary in order to draw a complete picture of an active region corona, given the careful handling of identified data (preparation) issues, which otherwise would mislead the event analysis and interpretation. Title: Plasma Upflows Induced by Magnetic Reconnection Above an Eruptive Flux Rope Authors: Baker, Deborah; Mihailescu, Teodora; Démoulin, Pascal; Green, Lucie M.; van Driel-Gesztelyi, Lidia; Valori, Gherardo; Brooks, David H.; Long, David M.; Janvier, Miho Bibcode: 2021SoPh..296..103B Altcode: 2021arXiv210616137B One of the major discoveries of Hinode's Extreme-ultraviolet Imaging Spectrometer (EIS) is the presence of upflows at the edges of active regions. As active regions are magnetically connected to the large-scale field of the corona, these upflows are a likely contributor to the global mass cycle in the corona. Here we examine the driving mechanism(s) of the very strong upflows with velocities in excess of 70 km s−1, known as blue-wing asymmetries, observed during the eruption of a flux rope in AR 10977 (eruptive flare SOL2007-12-07T04:50). We use Hinode/EIS spectroscopic observations combined with magnetic-field modeling to investigate the possible link between the magnetic topology of the active region and the strong upflows. A Potential Field Source Surface (PFSS) extrapolation of the large-scale field shows a quadrupolar configuration with a separator lying above the flux rope. Field lines formed by induced reconnection along the separator before and during the flux-rope eruption are spatially linked to the strongest blue-wing asymmetries in the upflow regions. The flows are driven by the pressure gradient created when the dense and hot arcade loops of the active region reconnect with the extended and tenuous loops overlying it. In view of the fact that separator reconnection is a specific form of the more general quasi-separatrix (QSL) reconnection, we conclude that the mechanism driving the strongest upflows is, in fact, the same as the one driving the persistent upflows of ≈10 - 20 km s−1 observed in all active regions. Title: The Evolution of Plasma Composition during a Solar Flare Authors: To, Andy S. H.; Long, David M.; Baker, Deborah; Brooks, David H.; van Driel-Gesztelyi, Lidia; Laming, J. Martin; Valori, Gherardo Bibcode: 2021ApJ...911...86T Altcode: 2021arXiv210209985T We analyze the coronal elemental abundances during a small flare using Hinode/EIS observations. Compared to the preflare elemental abundances, we observed a strong increase in coronal abundance of Ca XIV 193.84 Å, an emission line with low first ionization potential (FIP < 10 eV), as quantified by the ratio Ca/Ar during the flare. This is in contrast to the unchanged abundance ratio observed using Si X 258.38 Å/S X 264.23 Å. We propose two different mechanisms to explain the different composition results. First, the small flare-induced heating could have ionized S, but not the noble gas Ar, so that the flare-driven Alfvén waves brought up Si, S, and Ca in tandem via the ponderomotive force which acts on ions. Second, the location of the flare in strong magnetic fields between two sunspots may suggest fractionation occurred in the low chromosphere, where the background gas is neutral H. In this region, high-FIP S could behave more like a low-FIP than a high-FIP element. The physical interpretations proposed generate new insights into the evolution of plasma abundances in the solar atmosphere during flaring, and suggests that current models must be updated to reflect dynamic rather than just static scenarios. Title: Matching Temporal Signatures of Solar Features to Their Corresponding Solar-Wind Outflows Authors: de Pablos, D.; Long, D. M.; Owen, C. J.; Valori, G.; Nicolaou, G.; Harra, L. K. Bibcode: 2021SoPh..296...68D Altcode: 2021arXiv210309077D The role of small-scale coronal eruptive phenomena in the generation and heating of the solar wind remains an open question. Here, we investigate the role played by coronal jets in forming the solar wind by testing whether temporal variations associated with jetting in EUV intensity can be identified in the outflowing solar-wind plasma. This type of comparison is challenging due to inherent differences between remote-sensing observations of the source and in-situ observations of the outflowing plasma, as well as travel time and evolution of the solar wind throughout the heliosphere. To overcome these, we propose a novel algorithm combining signal filtering, two-step solar-wind ballistic back-mapping, window shifting, and Empirical Mode Decomposition. We first validate the method using synthetic data, before applying it to measurements from the Solar Dynamics Observatory and Wind spacecraft. The algorithm enables the direct comparison of remote-sensing observations of eruptive phenomena in the corona to in-situ measurements of solar-wind parameters, among other potential uses. After application to these datasets, we find several time windows where signatures of dynamics found in the corona are embedded in the solar-wind stream, at a time significantly earlier than expected from simple ballistic back-mapping, with the best-performing in-situ parameter being the solar-wind mass flux. Title: Spectropolarimetric fluctuations in a sunspot chromosphere Authors: Stangalini, M.; Baker, D.; Valori, G.; Jess, D. B.; Jafarzadeh, S.; Murabito, M.; To, A. S. H.; Brooks, D. H.; Ermolli, I.; Giorgi, F.; MacBride, C. D. Bibcode: 2021RSPTA.37900216S Altcode: 2020arXiv200905302S The instrumental advances made in this new era of 4 m class solar telescopes with unmatched spectropolarimetric accuracy and sensitivity will enable the study of chromospheric magnetic fields and their dynamics with unprecedented detail. In this regard, spectropolarimetric diagnostics can provide invaluable insight into magneto-hydrodynamic (MHD) wave processes. MHD waves and, in particular, Alfvénic fluctuations associated with particular wave modes were recently recognized as important mechanisms not only for the heating of the outer layers of the Sun's atmosphere and the acceleration of the solar wind, but also for the elemental abundance anomaly observed in the corona of the Sun and other Sun-like stars (also known as first ionization potential) effect. Here, we take advantage of state-of-the-art and unique spectropolarimetric Interferometric BIdimensional Spectrometer observations to investigate the relation between intensity and circular polarization (CP) fluctuations in a sunspot chromosphere. Our results show a clear link between the intensity and CP fluctuations in a patch which corresponds to a narrow range of magnetic field inclinations. This suggests the presence of Alfvénic perturbations in the sunspot.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: The Magnetic Environment of a Stealth Coronal Mass Ejection Authors: O'Kane, Jennifer; Mac Cormack, Cecilia; Mandrini, Cristina H.; Démoulin, Pascal; Green, Lucie M.; Long, David M.; Valori, Gherardo Bibcode: 2021ApJ...908...89O Altcode: 2020arXiv201203757O Interest in stealth coronal mass ejections (CMEs) is increasing due to their relatively high occurrence rate and space weather impact. However, typical CME signatures such as extreme-ultraviolet dimmings and post-eruptive arcades are hard to identify and require extensive image processing techniques. These weak observational signatures mean that little is currently understood about the physics of these events. We present an extensive study of the magnetic field configuration in which the stealth CME of 2011 March 3 occurred. Three distinct episodes of flare ribbon formation are observed in the stealth CME source active region (AR). Two occurred prior to the eruption and suggest the occurrence of magnetic reconnection that builds the structure that will become eruptive. The third occurs in a time close to the eruption of a cavity that is observed in STEREO-B 171 Å data; this subsequently becomes part of the propagating CME observed in coronagraph data. We use both local (Cartesian) and global (spherical) models of the coronal magnetic field, which are complemented and verified by the observational analysis. We find evidence of a coronal null point, with field lines computed from its neighborhood connecting the stealth CME source region to two ARs in the northern hemisphere. We conclude that reconnection at the null point aids the eruption of the stealth CME by removing the field that acted to stabilize the preeruptive structure. This stealth CME, despite its weak signatures, has the main characteristics of other CMEs, and its eruption is driven by similar mechanisms. Title: Flaring activity and related eruptions from active regions Authors: Green, Lucie; Long, David; Valori, Gherardo; O'Kane, Jennifer; James, Alexander Bibcode: 2021cosp...43E.992G Altcode: The Sun produces major eruptions, known as coronal mass ejections, from a range of heights in its atmosphere and across a range of kinematic and spatial scales. From compact, fast active region eruptions to high-altitude, slow stealth CMEs. These eruptions are the most energetic phenomena in the Solar System and CMEs that reach the Earth can create severe space events. Many studies have now shown that magnetic flux ropes are a fundamental component of the pre-eruption corona in some cases. In addition, a key role appears to be played by magnetic reconnection that evolves the pre-eruption corona from a sheared arcade to a flux rope configuration, which can then be destabilised by an ideal MHD process or by further magnetic reconnection. This talk will look CMEs originating in active regions covering the spectrum of events from energetic CMEs to low-energy stealth CMEs, and will ask whether there are common processes taking place across this wide range and whether flux ropes are involved in all cases. A long-term perspective will be given using observational and modelling results. The emergence of flux that forms the active region will be discussed along with the evolution of this flux via photospheric flows. Finally, thought will be given on the role of the ambient coronal field on the destabilisation of the CME structure. Title: Alfvénic Perturbations in a Sunspot Chromosphere Linked to Fractionated Plasma in the Corona Authors: Baker, Deborah; Stangalini, Marco; Valori, Gherardo; Brooks, David H.; To, Andy S. H.; van Driel-Gesztelyi, Lidia; Démoulin, Pascal; Stansby, David; Jess, David B.; Jafarzadeh, Shahin Bibcode: 2021ApJ...907...16B Altcode: 2020arXiv201204308B In this study, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modeling of the sunspot in order to probe the conditions that regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that, in the coronal magnetic field above the sunspot umbra, the plasma has photospheric composition. Coronal loops rooted in the penumbra contain fractionated plasma, with the highest levels observed in the loops that connect within the active region. Tracing field lines from regions of fractionated plasma in the corona to locations of Alfvénic fluctuations detected in the chromosphere shows that they are magnetically linked. These results indicate a connection between sunspot chromospheric activity and observable changes in coronal plasma composition. Title: Analysis of time-domain correlations between EUV and in-situ observations of coronal jets Authors: de Pablos, D.; Owen, C. J.; Long, D.; Harra, L. K.; Valori, G.; Nicolaou, G. Bibcode: 2020AGUFMSH0290018D Altcode: The role of small-scale coronal eruptive phenomena in the origin and heating of the solar wind remains an open question. In this work we attempt to determine the role played by coronal jets in forming the solar wind. This is a challenging problem due to inherent differences between remote-sensing observations of the source and in-situ observations of the outflowing plasma, as well as its travel time and evolution throughout the heliosphere. To overcome these challenges, we propose the use of Empirical Mode Decomposition to enable direct comparison of temporal signatures within remote sensing observations of eruptive phenomena in the corona and in-situ measurements of the solar wind. The technique is first validated using artificial data before being applied to measurements from the Solar Dynamics Observatory and Wind spacecraft. We discuss the potential reasons for discrepancies between results from the artificial data and observations at 1 AU, and their implications on the solar wind nature. Title: A new trigger mechanism for coronal mass ejections. The role of confined flares and photospheric motions in the formation of hot flux ropes Authors: James, A. W.; Green, L. M.; van Driel-Gesztelyi, L.; Valori, G. Bibcode: 2020A&A...644A.137J Altcode: 2020arXiv201011204J Context. Many previous studies have shown that the magnetic precursor of a coronal mass ejection (CME) takes the form of a magnetic flux rope, and a subset of them have become known as "hot flux ropes" due to their emission signatures in ∼10 MK plasma.
Aims: We seek to identify the processes by which these hot flux ropes form, with a view of developing our understanding of CMEs and thereby improving space weather forecasts.
Methods: Extreme-ultraviolet observations were used to identify five pre-eruptive hot flux ropes in the solar corona and study how they evolved. Confined flares were observed in the hours and days before each flux rope erupted, and these were used as indicators of episodic bursts of magnetic reconnection by which each flux rope formed. The evolution of the photospheric magnetic field was observed during each formation period to identify the process(es) that enabled magnetic reconnection to occur in the β < 1 corona and form the flux ropes.
Results: The confined flares were found to be homologous events and suggest flux rope formation times that range from 18 hours to 5 days. Throughout these periods, fragments of photospheric magnetic flux were observed to orbit around each other in sunspots where the flux ropes had a footpoint. Active regions with right-handed (left-handed) twisted magnetic flux exhibited clockwise (anticlockwise) orbiting motions, and right-handed (left-handed) flux ropes formed.
Conclusions: We infer that the orbital motions of photospheric magnetic flux fragments about each other bring magnetic flux tubes together in the corona, enabling component reconnection that forms a magnetic flux rope above a flaring arcade. This represents a novel trigger mechanism for solar eruptions and should be considered when predicting solar magnetic activity.

Movies associated to Figs. 4, 8, 12, and 14 are available at https://www.aanda.org Title: Metis - Solar Orbiter Topical Team on "Modelling of CME propagation/evolution in corona and solar wind in connection with Space Weather" Authors: Bemporad, A.; Banerjee, D.; Berlicki, A.; Biondo, R.; Boe, B.; Calchetti, D.; Capuano, G.; De Leo, Y.; Del Moro, D.; Feng, L.; Foldes, R.; Frassati, F.; Frazin, R. A.; Giovannelli, L.; Giunta, A. S.; Heinzel, P.; Ippolito, A.; Janvier, M.; Jerse, G.; Kilpua, K. E. J.; Laurenza, M.; Lloveras, D.; Magdalenic, J.; Mancuso, S.; Messerotti, M.; Mierla, M.; Nandy, D.; Napoletano, G.; Nuevo, F.; Pagano, P.; Pinto, R.; Plainaki, C.; Reale, F.; Romoli, M.; Rodriguez, L.; Slemer, A.; Spadaro, D.; Susino, R.; Stangalini, M.; Vainio, R. O.; Valori, G.; Vásquez, A. M.; West, M. J. Bibcode: 2020AGUFMSH0360027B Altcode: Despite the current availability of multi-spacecraft observations of Coronal Mass Ejections (CMEs) and their interplanetary counterpart (ICMEs), at present we still don't understand which physical phenomena are driving their expansion and propagation phases. This also limits our understanding on how CMEs (observed with remote sensing data) become ICMEs (observed in situ), how they interact with the background solar wind, and how their final geo-effectiveness can be modified during their interplanetary evolution. Such problems match some of the scientific objectives of the Solar Orbiter Science Activity Plan and of the Metis coronagraph. Thanks to its multi-channel capability, Metis (acquiring images in the visible light and at the same time in the UV HI Lyman-alpha emission) will really provide an unprecedented view of CMEs and in particular of their thermodynamic evolution. At closest approaches to the Sun (in the nominal mission), Metis will acquire high spatial resolution and/or temporal cadence multi-channel images of CMEs. Farther from the Sun, Metis will shed light on the early Interplanetary propagation of CMEs. Later on (in the extended mission) Metis will observe for the first time the CME/ICME propagation out-of-ecliptic. These novelties will be combined with the unique vantage point that will be offered by the Solar Orbiter spacecraft, and supported with valuable data acquired by other on-board remote sensing (e.g. SPICE, EUI, SoloHI) and in situ (e.g. EPD, MAG, SWA, RPW) instruments. In this contribution we present the ongoing activities of the Metis Topical Team on "CME/ICME propagation", (http://metis.oato.inaf.it/topical_teams.html), an international working group recently established and gathering scientists from different countries, experts of both in-situ and remote sensing observations, as well as numerical simulations, and we summarize the main science objectives discussed during the last months. Title: Additivity of relative magnetic helicity in finite volumes Authors: Valori, Gherardo; Démoulin, Pascal; Pariat, Etienne; Yeates, Anthony; Moraitis, Kostas; Linan, Luis Bibcode: 2020A&A...643A..26V Altcode: 2020arXiv200800968V Context. Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint on the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, in other words that it is an additive quantity. A limited number of very specific applications have shown that this is not the case.
Aims: Progress in understanding the nonadditivity of relative magnetic helicity requires removal of restrictive assumptions in favor of a general formalism that can be used in both theoretical investigations and numerical applications.
Methods: We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge.
Results: We prove the nonadditivity of relative magnetic helicity in finite volumes in the most general, gauge-invariant formalism, and verify this numerically. We adopt more restrictive assumptions to derive known specific approximations, which yields a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the nonadditivity term in the partition equation is, in general, non-negligible.
Conclusions: The nonadditivity of relative magnetic helicity can potentially be a serious impediment to the application of relative helicity conservation as a constraint on the complex dynamics of magnetized plasmas. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of nonadditivity on global helicity budgets of complex physical processes. Title: Erratum: "On the Reliability of Magnetic Energy and Helicity Computations Based on Nonlinear Force-free Coronal Magnetic Field Models" (2019, ApJL, 880, L6) Authors: Thalmann, Julia K.; Linan, L.; Pariat, E.; Valori, G. Bibcode: 2020ApJ...902L..48T Altcode: No abstract at ADS Title: Study of the spatial association between an active region jet and a nonthermal type~${\rm III}$ radio burst Authors: Mulay, Sargam M.; Sharma, Rohit; Valori, Gherardo; Vásquez, Alberto M.; Del Zanna, Giulio; Mason, Helen; Oberoi, Divya Bibcode: 2020arXiv200914581M Altcode: We aim to investigate the spatial location of the source of an active region (AR) jet and its relation with associated nonthermal type~III radio emission. An emission measure (EM) method was used to study the thermodynamic nature of the AR jet. The nonthermal type~{\rm III} radio burst observed at meterwavelength was studied using the Murchison Widefield Array (MWA) radio imaging and spectroscopic data. The local configuration of the magnetic field and the connectivity of the source region of the jet with open magnetic field structures was studied using a nonlinear force-free field (NLFFF) extrapolation and potential field source surface (PFSS) extrapolation respectively. The plane-of-sky velocity of the AR jet was found to be $\sim$136~km/s. The EM analysis confirmed the presence of low temperature 2~MK plasma for the spire, whereas hot plasma, between 5-8 MK, was present at the footpoint region which also showed the presence of Fe~{\sc xviii} emission. A lower limit on the electron number density was found to be 1.4$\times$10$^{8}$ cm$^{-3}$ for the spire and 2.2$\times$10$^{8}$~cm$^{-3}$ for the footpoint. A temporal and spatial correlation between the AR jet and nonthermal type III burst confirmed the presence of open magnetic fields. An NLFFF extrapolation showed that the photospheric footpoints of the null point were anchored at the location of the source brightening of the jet. The spatial location of the radio sources suggests an association with the extrapolated closed and open magnetic fields although strong propagation effects are also present. The multi-scale analysis of the field at local, AR, and solar scales confirms the interlink between different flux bundles involved in the generation of the type III radio signal with flux transferred from a small coronal hole to the periphery of the sunspot via null point reconnection with an emerging structure. Title: The Magnetic Environment of a Stealth CME Authors: O'Kane, J.; Mandrini, C.; Demoulin, P.; Green, L.; Valori, G.; Long, D. Bibcode: 2020SPD....5121005O Altcode: Interest in Stealth Coronal Mass Ejections (CMEs) is increasing due to their relatively high occurrence rate and space weather impact. However, typical CME signatures such as EUV dimmings and post-eruptive arcades are hard to identify for stealth CMEs and require extensive image processing techniques. These weak observational signatures mean little is currently understood about the physics of these events. We present an extensive study of the magnetic field configuration in which the stealth CME of 3 March 2011 occurred. The magnetic field prior to the eruption is evaluated using a Linear Force Free Field (LFFF) model and a Potential Field Source Surface (PFSS) model, and complemented by in-depth observational analysis. The models are verified using observations of plasma emission structures in the stealth CME source region and trans-equatorial loops. We find evidence of a high-altitude null point in both the LFFF model and the PFSS model, with surrounding field lines connecting two active regions on the solar disk. One of these active regions in the Southern Hemisphere is shown to be the source region of the stealth CME. Three distinct episodes of flare ribbon formation are observed in AIA 304Å. Two occurred prior to the eruption and suggest the occurrence of magnetic reconnection that builds the eruptive structure. The third occurs at the same time as an erupting cavity is observed in STEREO-B 171Å data; this subsequently becomes part of the propagating CME observed in COR1. We conclude that reconnection at the null point, driven by eruptive activity in the complex northern active region, aids the eruption of the stealth CME by removing field that acted to stabilise the pre-eruptive structure. Title: Modelado magnético de regiones activas solares: Una comparación entre dos modelos libres de fuerzas Authors: Nuevo, F. A.; Valori, G.; López Fuentes, M.; Mandrini, C. H.; Vásquez, A. M. Bibcode: 2020BAAA...61B...7N Altcode: The knowledge of the three-dimensional coronal magnetic field ($\mathbf{B}$) at high spatial resolution is key to better understand the physical mechanisms that trigger active phenomena in the corona, the main drivers of { space weather}. High resolution, direct coronal measurements of $\mathbf{B}$ are not available, so we must rely on suitable coronal field models based on the available photospheric field measurements (magnetograms). For active region (AR) magnetic fields, where { magnetic pressure is much larger than plasma pressure}, the force-free regime ($\nabla\times\mathbf{B} = \alpha \mathbf{B}$) is a valid approximation. Force-free field models for which the $\alpha$ parameter is a constant are called Linear (LFFF) and models for which $\alpha$ is a function of { the} position are called non-linear (NLFFF).In this work we test and compare specific numerical implementations of both LFFF and NLFFF models applied to two ARs. Title: Can Subphotospheric Magnetic Reconnection Change the Elemental Composition in the Solar Corona? Authors: Baker, Deborah; van Driel-Gesztelyi, Lidia; Brooks, David H.; Démoulin, Pascal; Valori, Gherardo; Long, David M.; Laming, J. Martin; To, Andy S. H.; James, Alexander W. Bibcode: 2020ApJ...894...35B Altcode: 2020arXiv200303325B Within the coronae of stars, abundances of those elements with low first ionization potential (FIP) often differ from their photospheric values. The coronae of the Sun and solar-type stars mostly show enhancements of low-FIP elements (the FIP effect) while more active stars such as M dwarfs have coronae generally characterized by the inverse-FIP effect (I-FIP). Here we observe patches of I-FIP effect solar plasma in AR 12673, a highly complex βγδ active region. We argue that the umbrae of coalescing sunspots, and more specifically strong light bridges within the umbrae, are preferential locations for observing I-FIP effect plasma. Furthermore, the magnetic complexity of the active region and major episodes of fast flux emergence also lead to repetitive and intense flares. The induced evaporation of the chromospheric plasma in flare ribbons crossing umbrae enables the observation of four localized patches of I-FIP effect plasma in the corona of AR 12673. These observations can be interpreted in the context of the ponderomotive force fractionation model which predicts that plasma with I-FIP effect composition is created by the refraction of waves coming from below the chromosphere. We propose that the waves generating the I-FIP effect plasma in solar active regions are generated by subphotospheric reconnection of coalescing flux systems. Although we only glimpse signatures of I-FIP effect fractionation produced by this interaction in patches on the Sun, on highly active M stars it may be the dominant process. Title: Energy and helicity fluxes in line-tied eruptive simulations Authors: Linan, L.; Pariat, É.; Aulanier, G.; Moraitis, K.; Valori, G. Bibcode: 2020A&A...636A..41L Altcode: 2020arXiv200301698L Context. Conservation properties of magnetic helicity and energy in the quasi-ideal and low-β solar corona make these two quantities relevant for the study of solar active regions and eruptions.
Aims: Based on a decomposition of the magnetic field into potential and nonpotential components, magnetic energy and relative helicity can both also be decomposed into two quantities: potential and free energies, and volume-threading and current-carrying helicities. In this study, we perform a coupled analysis of their behaviors in a set of parametric 3D magnetohydrodynamic (MHD) simulations of solar-like eruptions.
Methods: We present the general formulations for the time-varying components of energy and helicity in resistive MHD. We calculated them numerically with a specific gauge, and compared their behaviors in the numerical simulations, which differ from one another by their imposed boundary-driving motions. Thus, we investigated the impact of different active regions surface flows on the development of the energy and helicity-related quantities.
Results: Despite general similarities in their overall behaviors, helicities and energies display different evolutions that cannot be explained in a unique framework. While the energy fluxes are similar in all simulations, the physical mechanisms that govern the evolution of the helicities are markedly distinct from one simulation to another: the evolution of volume-threading helicity can be governed by boundary fluxes or helicity transfer, depending on the simulation.
Conclusions: The eruption takes place for the same value of the ratio of the current-carrying helicity to the total helicity in all simulations. However, our study highlights that this threshold can be reached in different ways, with different helicity-related processes dominating for different photospheric flows. This means that the details of the pre-eruptive dynamics do not influence the eruption-onset helicity-related threshold. Nevertheless, the helicity-flux dynamics may be more or less efficient in changing the time required to reach the onset of the eruption. Title: Study of the spatial association between an active region jet and a nonthermal type III radio burst Authors: Mulay, Sargam M.; Sharma, Rohit; Valori, Gherardo; Vásquez, Alberto M.; Del Zanna, Giulio; Mason, Helen; Oberoi, Divya Bibcode: 2019A&A...632A.108M Altcode:
Aims: We aim to investigate the spatial location of the source of an active region (AR) jet and its relation with associated nonthermal type III radio emission.
Methods: An emission measure (EM) method was used to study the thermodynamic nature of the AR jet. The nonthermal type III radio burst observed at meterwavelength was studied using the Murchison Widefield Array (MWA) radio imaging and spectroscopic data. The local configuration of the magnetic field and the connectivity of the source region of the jet with open magnetic field structures was studied using a nonlinear force-free field (NLFFF) extrapolation and potential field source surface (PFSS) extrapolation respectively.
Results: The plane-of-sky velocity of the AR jet was found to be ∼136 km s-1. The EM analysis confirmed the presence of low temperature 2 MK plasma for the spire, whereas hot plasma, between 5 and 8 MK, was present at the footpoint region which also showed the presence of Fe XVIII emission. A lower limit on the electron number density was found to be 1.4 × 108 cm-3 for the spire and 2.2 × 108 cm-3 for the footpoint. A temporal and spatial correlation between the AR jet and nonthermal type III burst confirmed the presence of open magnetic fields. An NLFFF extrapolation showed that the photospheric footpoints of the null point were anchored at the location of the source brightening of the jet. The spatial location of the radio sources suggests an association with the extrapolated closed and open magnetic fields although strong propagation effects are also present.
Conclusions: The multi-scale analysis of the field at local, AR, and solar scales confirms the interlink between different flux bundles involved in the generation of the type III radio signal with flux transferred from a small coronal hole to the periphery of the sunspot via null point reconnection with an emerging structure.

The movie associated to Fig. 4 is available at https://www.aanda.org Title: Magnetic Helicity Budget of Solar Active Regions Prolific of Eruptive and Confined Flares Authors: Thalmann, Julia K.; Moraitis, K.; Linan, L.; Pariat, E.; Valori, G.; Dalmasse, K. Bibcode: 2019ApJ...887...64T Altcode: 2019arXiv191006563T We compare the coronal magnetic energy and helicity of two solar active regions (ARs), prolific in major eruptive (AR 11158) and confined (AR 12192) flaring, and analyze the potential of deduced proxies to forecast upcoming flares. Based on nonlinear force-free (NLFF) coronal magnetic field models with a high degree of solenoidality, and applying three different computational methods to investigate the coronal magnetic helicity, we are able to draw conclusions with a high level of confidence. Based on real observations of two solar ARs we checked trends regarding the potential eruptivity of the active-region corona, as suggested earlier in works that were based on numerical simulations, or solar observations. Our results support that the ratio of current-carrying to total helicity, | {H}{{J}}| /| {H}{ \mathcal V }| , shows a strong ability to indicate the eruptive potential of a solar AR. However, | {H}{{J}}| /| {H}{ \mathcal V }| does not seem to be indicative for the magnitude or type of an upcoming flare (confined or eruptive). Interpreted in the context of earlier observational studies, our findings furthermore support that the total relative helicity normalized to the magnetic flux at the NLFF model’s lower boundary, {H}{ \mathcal V }/{φ }2, represents no indicator for the eruptivity. Title: Quantifying the Relationship between Moreton-Ramsey Waves and “EIT Waves” Using Observations of Four Homologous Wave Events Authors: Long, David M.; Jenkins, Jack; Valori, Gherardo Bibcode: 2019ApJ...882...90L Altcode: 2019arXiv190707963L Freely propagating global waves in the solar atmosphere are commonly observed using extreme ultraviolet passbands (EUV or “EIT waves”), and less regularly in H-alpha (Moreton-Ramsey waves). Despite decades of research, joint observations of EUV and Moreton-Ramsey waves remain rare, complicating efforts to quantify the connection between these phenomena. We present observations of four homologous global waves originating from the same active region between 2014 March 28 and 30 and observed using both EUV and H-alpha data. Each global EUV wave was observed by the Solar Dynamics Observatory, with the associated Moreton-Ramsey waves identified using the Global Oscillations Network Group network. All of the global waves exhibit high initial velocity (e.g., 842-1388 km s-1 in the 193 Å passband) and strong deceleration (e.g., -1437 to -782 m s-2 in the 193 Å passband) in each of the EUV passbands studied, with the EUV wave kinematics exceeding those of the Moreton-Ramsey wave. The density compression ratio of each global wave was estimated using both differential emission measure and intensity variation techniques, with both indicating that the observed waves were weakly shocked with a fast magnetosonic Mach number slightly greater than one. This suggests that, according to current models, the global coronal waves were not strong enough to produce Moreton-Ramsey waves, indicating an alternative explanation for these observations. Instead, we conclude that the evolution of the global waves was restricted by the surrounding coronal magnetic field, in each case producing a downward-angled wavefront propagating toward the north solar pole, which perturbed the chromosphere and was observed as a Moreton-Ramsey wave. Title: On the Reliability of Magnetic Energy and Helicity Computations Based on Nonlinear Force-free Coronal Magnetic Field Models Authors: Thalmann, Julia K.; Linan, L.; Pariat, E.; Valori, G. Bibcode: 2019ApJ...880L...6T Altcode: 2019arXiv190701179T We demonstrate the sensitivity of magnetic energy and helicity computations regarding the quality of the underlying coronal magnetic field model. We apply the method of Wiegelmann & Inhester to a series of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms, and discuss nonlinear force-free (NLFF) solutions based on two different sets of the free model parameters. The two time series differ from each other concerning their force-free and solenoidal quality. Both force- and divergence-freeness are required for a consistent NLFF solution. Full satisfaction of the solenoidal property is inherent in the definition of relative magnetic helicity in order to ensure gauge independence. We apply two different magnetic helicity computation methods to both NLFF time series and find that the output is highly dependent on the level to which the NLFF magnetic fields satisfy the divergence-free condition, with the computed magnetic energy being less sensitive than the relative helicity. Proxies for the nonpotentiality and eruptivity derived from both quantities are also shown to depend strongly on the solenoidal property of the NLFF fields. As a reference for future applications, we provide quantitative thresholds for the force- and divergence-freeness, for the assurance of reliable computation of magnetic energy and helicity, and of their related eruptivity proxies. Title: Relative magnetic field line helicity Authors: Moraitis, K.; Pariat, E.; Valori, G.; Dalmasse, K. Bibcode: 2019A&A...624A..51M Altcode: 2019arXiv190210410M Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of magnetic helicity is given by the field line helicity, which expresses the amount of helicity associated to individual field lines rather than in the full analysed volume.
Aims: Magnetic helicity is not a gauge-invariant quantity in general, unless it is computed with respect to a reference field, yielding the so-called relative magnetic helicity. The field line helicity corresponding to the relative magnetic helicity has only been examined under specific conditions so far. This work aims to define the field line helicity corresponding to relative magnetic helicity in the most general way. In addition to its general form, we provide the expression for the relative magnetic field line helicity in a few commonly used gauges, and reproduce known results as a limit of our general formulation.
Methods: By starting from the definition of relative magnetic helicity, we derived the corresponding field line helicity, and we noted the assumptions on which it is based.
Results: We checked that the developed quantity reproduces relative magnetic helicity by using three different numerical simulations. For these cases we also show the morphology of field line helicity in the volume, and on the photospheric plane. As an application to solar situations, we compared the morphology of field line helicity on the photosphere with that of the connectivity-based helicity flux density in two reconstructions of an active region's magnetic field. We discuss how the derived relative magnetic field line helicity has a wide range of applications, notably in solar physics and magnetic reconnection studies. Title: Transient Inverse-FIP Plasma Composition Evolution within a Solar Flare Authors: Baker, Deborah; van Driel-Gesztelyi, Lidia; Brooks, David H.; Valori, Gherardo; James, Alexander W.; Laming, J. Martin; Long, David M.; Démoulin, Pascal; Green, Lucie M.; Matthews, Sarah A.; Oláh, Katalin; Kővári, Zsolt Bibcode: 2019ApJ...875...35B Altcode: 2019arXiv190206948B Understanding elemental abundance variations in the solar corona provides an insight into how matter and energy flow from the chromosphere into the heliosphere. Observed variations depend on the first ionization potential (FIP) of the main elements of the Sun’s atmosphere. High-FIP elements (>10 eV) maintain photospheric abundances in the corona, whereas low-FIP elements have enhanced abundances. Conversely, inverse FIP (IFIP) refers to the enhancement of high-FIP or depletion of low-FIP elements. We use spatially resolved spectroscopic observations, specifically the Ar XIV/Ca XIV intensity ratio, from Hinode’s Extreme-ultraviolet Imaging Spectrometer to investigate the distribution and evolution of plasma composition within two confined flares in a newly emerging, highly sheared active region. During the decay phase of the first flare, patches above the flare ribbons evolve from the FIP to the IFIP effect, while the flaring loop tops show a stronger FIP effect. The patch and loop compositions then evolve toward the preflare basal state. We propose an explanation of how flaring in strands of highly sheared emerging magnetic fields can lead to flare-modulated IFIP plasma composition over coalescing umbrae which are crossed by flare ribbons. Subsurface reconnection between the coalescing umbrae leads to the depletion of low-FIP elements as a result of an increased wave flux from below. This material is evaporated when the flare ribbons cross the umbrae. Our results are consistent with the ponderomotive fractionation model for the creation of IFIP-biased plasma. Title: Modeling the Effect of Mass-draining on Prominence Eruptions Authors: Jenkins, Jack M.; Hopwood, Matthew; Démoulin, Pascal; Valori, Gherardo; Aulanier, Guillaume; Long, David M.; van Driel-Gesztelyi, Lidia Bibcode: 2019ApJ...873...49J Altcode: 2019arXiv190110970J Quiescent solar prominences are observed within the solar atmosphere for up to several solar rotations. Their eruption is commonly preceded by a slow increase in height that can last from hours to days. This increase in the prominence height is believed to be due to their host magnetic flux rope transitioning through a series of neighboring quasi-equilibria before the main loss of equilibrium that drives the eruption. Recent work suggests that the removal of prominence mass from a stable, quiescent flux rope is one possible cause for this change in height. However, these conclusions are drawn from observations and are subject to interpretation. Here, we present a simple model to quantify the effect of “mass-draining” during the pre-eruptive height evolution of a solar flux rope. The flux rope is modeled as a line current suspended within a background potential magnetic field. We first show that the inclusion of mass, up to 1012 kg, can modify the height at which the line current experiences loss of equilibrium by up to 14%. Next, we show that the rapid removal of mass prior to the loss of equilibrium can allow the height of the flux rope to increase sharply and without an upper bound as it approaches its loss-of-equilibrium point. This indicates that the critical height for the loss of equilibrium can occur at a range of heights depending explicitly on the amount and evolution of mass within the flux rope. Finally, we demonstrate that for the same amount of drained mass, the effect on the height of the flux rope is up to two orders of magnitude larger for quiescent prominences than for active region prominences. Title: An Observationally Constrained Model of a Flux Rope that Formed in the Solar Corona Authors: James, Alexander W.; Valori, Gherardo; Green, Lucie M.; Liu, Yang; Cheung, Mark C. M.; Guo, Yang; van Driel-Gesztelyi, Lidia Bibcode: 2018csc..confE...9J Altcode: Coronal mass ejections (CMEs) are large-scale eruptions of plasma from the coronae of stars, and it is important to study the plasma processes involved in their initiation. This first requires us to understand the pre-eruptive configuration of CMEs. To this end, we used extreme-ultraviolet (EUV) observations from SDO/AIA to conclude that a magnetic flux rope formed high-up in the solar corona above NOAA Active Region 11504 before it erupted on 2012 June 14. Then, we used data from SDO/HMI and our knowledge of the EUV observations to model the coronal magnetic field of the active region one hour prior to eruption using a nonlinear force-free field extrapolation. The extrapolation revealed a flux rope that matches the EUV observations remarkably well, with its axis 120 Mm above the photosphere. The erupting structure was not observed to kink, but the decay index near the apex of the axis of the extrapolated flux rope is comparable to typical critical values required for the onset of the torus instability. Therefore, we suggest that the torus instability drove the eruption of the flux rope. Title: Multi-wavelength observations of 4 homologous global coronal waves Authors: Long, David; Lawless, Julia; Valori, Gherardo; Jenkins, Jack Bibcode: 2018csc..confE..15L Altcode: Global coronal waves (commonly called "EIT waves") were first observed by SOHO/EIT in 1997 and are now considered to be large-scale shock fronts initially driven by the rapid expansion of an erupting coronal mass ejection in the low corona. I will present observations of four homologous global waves which erupted from the same active region over the course of three days in March 2014. Each global EUV wave was well observed by SDO/AIA and was associated with a H-alpha Moreton-Ramsey wave observed at high cadence by the GONG network. These observations provide the opportunity to directly relate global waves in EUV and H-alpha observations with high cadence and answer a fundamental question about the relationship between these phenomena which has persisted since they were first observed. Title: Time Variations of the Nonpotential and Volume-threading Magnetic Helicities Authors: Linan, L.; Pariat, É.; Moraitis, K.; Valori, G.; Leake, J. Bibcode: 2018ApJ...865...52L Altcode: 2018arXiv180903765L Relative magnetic helicity is a gauge-invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge-invariant quantities, the magnetic helicity of the nonpotential component of the field and a complementary volume-threading helicity. Recent analysis of numerical experiments simulating the generation of solar eruptions have shown that the ratio of the nonpotential helicity to the total relative helicity is a clear marker of the eruptivity of the magnetic system, and that the high value of that quantity could be a sufficient condition for the onset of the instability generating the eruptions. The present study introduces the first analytical examination of the time variations of these nonpotential and volume-threading helicities. The validity of the analytical formulae derived are confirmed with analysis of 3D magnetohydrodynamics (MHD) simulations of solar coronal dynamics. Both the analytical investigation and the numerical application show that, unlike magnetic helicity, the nonpotential and the volume-threading helicities are not conserved quantities, even in the ideal MHD regime. A term corresponding to the transformation between the nonpotential and volume-threading helicities frequently dominates their dynamics. This finding has an important consequence for their estimation in the solar corona: unlike with relative helicity, their volume coronal evolution cannot be ascertained by the flux of these quantities through the volume’s boundaries. Only techniques extrapolating the 3D coronal field will enable both the proper study of the nonpotential and volume-threading helicities and the observational analysis of helicity-based solar-eruptivity proxies. Title: Threshold of Non-potential Magnetic Helicity Ratios at the Onset of Solar Eruptions Authors: Zuccarello, F. P.; Pariat, E.; Valori, G.; Linan, L. Bibcode: 2018ApJ...863...41Z Altcode: 2018arXiv180700532Z The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions. The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic helicity in the corona and if and how well magnetic-helicity-related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, and peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic helicity and the total relative magnetic helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such a threshold is not observed for other quantities as, for example, those related to the magnetic energy. Title: Computation of Relative Magnetic Helicity in Spherical Coordinates Authors: Moraitis, Kostas; Pariat, Étienne; Savcheva, Antonia; Valori, Gherardo Bibcode: 2018SoPh..293...92M Altcode: 2018arXiv180603011M Magnetic helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, helicity is only treated approximately. We present here a method for properly computing the relative magnetic helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method. Title: An Observationally Constrained Model of a Flux Rope that Formed in the Solar Corona Authors: James, Alexander W.; Valori, Gherardo; Green, Lucie M.; Liu, Yang; Cheung, Mark C. M.; Guo, Yang; van Driel-Gesztelyi, Lidia Bibcode: 2018ApJ...855L..16J Altcode: 2018arXiv180207965J Coronal mass ejections (CMEs) are large-scale eruptions of plasma from the coronae of stars. Understanding the plasma processes involved in CME initiation has applications for space weather forecasting and laboratory plasma experiments. James et al. used extreme-ultraviolet (EUV) observations to conclude that a magnetic flux rope formed in the solar corona above NOAA Active Region 11504 before it erupted on 2012 June 14 (SOL2012-06-14). In this work, we use data from the Solar Dynamics Observatory (SDO) to model the coronal magnetic field of the active region one hour prior to eruption using a nonlinear force-free field extrapolation, and find a flux rope reaching a maximum height of 150 Mm above the photosphere. Estimations of the average twist of the strongly asymmetric extrapolated flux rope are between 1.35 and 1.88 turns, depending on the choice of axis, although the erupting structure was not observed to kink. The decay index near the apex of the axis of the extrapolated flux rope is comparable to typical critical values required for the onset of the torus instability, so we suggest that the torus instability drove the eruption. Title: Studying the Transfer of Magnetic Helicity in Solar Active Regions with the Connectivity-based Helicity Flux Density Method Authors: Dalmasse, K.; Pariat, É.; Valori, G.; Jing, J.; Démoulin, P. Bibcode: 2018ApJ...852..141D Altcode: 2017arXiv171204691D In the solar corona, magnetic helicity slowly and continuously accumulates in response to plasma flows tangential to the photosphere and magnetic flux emergence through it. Analyzing this transfer of magnetic helicity is key for identifying its role in the dynamics of active regions (ARs). The connectivity-based helicity flux density method was recently developed for studying the 2D and 3D transfer of magnetic helicity in ARs. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity, which allows it to faithfully track the photospheric flux of magnetic helicity. Because the magnetic field is not measured in the solar corona, modeled 3D solutions obtained from force-free magnetic field extrapolations must be used to derive the magnetic connectivity. Different extrapolation methods can lead to markedly different 3D magnetic field connectivities, thus questioning the reliability of the connectivity-based approach in observational applications. We address these concerns by applying this method to the isolated and internally complex AR 11158 with different magnetic field extrapolation models. We show that the connectivity-based calculations are robust to different extrapolation methods, in particular with regard to identifying regions of opposite magnetic helicity flux. We conclude that the connectivity-based approach can be reliably used in observational analyses and is a promising tool for studying the transfer of magnetic helicity in ARs and relating it to their flaring activity. Title: Non-thermal distributions and energy transport in the solar flares Authors: Matthews, Sarah; del Zanna, Guilio; Calcines, Ariadna; Mason, Helen; Mathioudakis, Mihalis; Culhane, Len; Harra, Louise; van Driel-Gesztelyi, Lidia; Green, Lucie; Long, David; Baker, Deb; Valori, Gherardo Bibcode: 2017arXiv171200773M Altcode: Determining the energy transport mechanisms in flares remains a central goal in solar flares physics that is still not adequately answered by the 'standard flare model'. In particular, the relative roles of particles and/or waves as transport mechanisms, the contributions of low energy protons and ions to the overall flare budget, and the limits of low energy non-thermal electron distribution are questions that still cannot be adequately reconciled with current instrumentation. In this 'White Paper' submitted in response to the call for inputs to the Next Generation Solar Physics Mission review process initiated by JAXA, NASA and ESA in 2016, we outline the open questions in this area and possible instrumentation that could provide the required observations to help answer these and other flare-related questions. Title: Measuring the magnetic field of a trans-equatorial loop system using coronal seismology (Corrigendum) Authors: Long, D. M.; Valori, G.; Pérez-Suárez, D.; Morton, R. J.; Vásquez, A. M. Bibcode: 2017A&A...607C...3L Altcode: No abstract at ADS Title: The 2013 February 17 Sunquake in the Context of the Active Region's Magnetic Field Configuration Authors: Green, L. M.; Valori, G.; Zuccarello, F. P.; Zharkov, S.; Matthews, S. A.; Guglielmino, S. L. Bibcode: 2017ApJ...849...40G Altcode: 2017arXiv170904874G Sunquakes are created by the hydrodynamic response of the lower atmosphere to a sudden deposition of energy and momentum. In this study, we investigate a sunquake that occurred in NOAA active region 11675 on 2013 February 17. Observations of the corona, chromosphere, and photosphere are brought together for the first time with a nonlinear force-free model of the active region’s magnetic field in order to probe the magnetic environment in which the sunquake was initiated. We find that the sunquake was associated with the destabilization of a flux rope and an associated M-class GOES flare. Active region 11675 was in its emergence phase at the time of the sunquake and photospheric motions caused by the emergence heavily modified the flux rope and its associated quasi-separatrix layers, eventually triggering the flux rope’s instability. The flux rope was surrounded by an extended envelope of field lines rooted in a small area at the approximate position of the sunquake. We argue that the configuration of the envelope, by interacting with the expanding flux rope, created a “magnetic lens” that may have focussed energy on one particular location of the photosphere, creating the necessary conditions for the initiation of the sunquake. Title: Flux rope, hyperbolic flux tube, and late extreme ultraviolet phases in a non-eruptive circular-ribbon flare Authors: Masson, Sophie; Pariat, Étienne; Valori, Gherardo; Deng, Na; Liu, Chang; Wang, Haimin; Reid, Hamish Bibcode: 2017A&A...604A..76M Altcode: 2017arXiv170401450M Context. The dynamics of ultraviolet (UV) emissions during solar flares provides constraints on the physical mechanisms involved in the trigger and the evolution of flares. In particular it provides some information on the location of the reconnection sites and the associated magnetic fluxes. In this respect, confined flares are far less understood than eruptive flares generating coronal mass ejections.
Aims: We present a detailed study of a confined circular flare dynamics associated with three UV late phases in order to understand more precisely which topological elements are present and how they constrain the dynamics of the flare.
Methods: We perform a non-linear force-free field extrapolation of the confined flare observed with the Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) instruments on board Solar Dynamics Observatory (SDO). From the 3D magnetic field we compute the squashing factor and we analyse its distribution. Conjointly, we analyse the AIA extreme ultraviolet (EUV) light curves and images in order to identify the post-flare loops, and their temporal and thermal evolution. By combining the two analyses we are able to propose a detailed scenario that explains the dynamics of the flare.
Results: Our topological analysis shows that in addition to a null-point topology with the fan separatrix, the spine lines and its surrounding quasi-separatix layer (QSL) halo (typical for a circular flare), a flux rope and its hyperbolic flux tube (HFT) are enclosed below the null. By comparing the magnetic field topology and the EUV post-flare loops we obtain an almost perfect match between the footpoints of the separatrices and the EUV 1600 Å ribbons and between the HFT field line footpoints and bright spots observed inside the circular ribbons. We show, for the first time in a confined flare, that magnetic reconnection occurred initially at the HFT below the flux rope. Reconnection at the null point between the flux rope and the overlying field is only initiated in a second phase. In addition, we showed that the EUV late phase observed after the main flare episode is caused by the cooling loops of different length which have all reconnected at the null point during the impulsive phase.
Conclusions: Our analysis shows in one example that flux ropes are present in null-point topology not only for eruptive and jet events, but also for confined flares. This allows us to conjecture on the analogies between conditions that govern the generation of jets, confined flares or eruptive flares.

A movie is available at http://www.aanda.org Title: Studying the transfer of magnetic helicity in solar active regions Authors: Dalmasse, Kevin; Valori, Gherardo; Jing, Ju; Pariat, Etienne; Demoulin, Pascal Bibcode: 2017SPD....4811206D Altcode: Analyzing the transfer of magnetic helicity in active regions is a key component for understanding the nature of its coronal storage and release and for identifying its role in the coronal dynamics of active regions. We recently developed a method for studying the photospheric flux of magnetic helicity in both 2D and 3D. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity. Since the coronal magnetic field in active regions is not measured, we rely on the non-unique 3D solution obtained from force-free coronal magnetic field extrapolations to derive the magnetic field connectivity. In this poster, we apply the method to the complex and highly-flaring active region NOAA 11158 using the magnetic field connectivity derived from different force-free extrapolation models and implementations. We show that the calculations of photospheric flux of magnetic helicity are robust to different extrapolation methods and assumptions, in particular with regards to identifying regions of opposite magnetic helicity flux. Finally, we discuss the implications of our results for tracking the transfer of magnetic helicity in active regions and relate it to their flaring activity. Title: Studying the transfer of magnetic helicity in solar active regions Authors: Dalmasse, Kévin; Jing, J.; Pariat, E.; Valori, G.; Démoulin, P. Bibcode: 2017shin.confE.160D Altcode: Analyzing the transfer of magnetic helicity in active regions is a key component for understanding the nature of its coronal storage and release and for identifying its role in the coronal dynamics of active regions. We recently developed a method for studying the photospheric flux of magnetic helicity in both 2D and 3D. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity. Since the coronal magnetic field in active regions is not measured, we rely on the approximate 3D solution obtained from force-free coronal magnetic field extrapolations to derive the magnetic field connectivity. In this poster, we apply the method to the complex and highly-flaring active region NOAA 11158 using the magnetic field connectivity derived from different force-free extrapolation models and implementations. We show that the calculations of photospheric flux of magnetic helicity are robust to different extrapolation methods and assumptions, in particular with regards to identifying regions of opposite magnetic helicity flux. Finally, we discuss the implications of our results for tracking the transfer of magnetic helicity in active regions and relate it to their flaring activity. Title: Measuring the magnetic field of a trans-equatorial loop system using coronal seismology Authors: Long, D. M.; Valori, G.; Pérez-Suárez, D.; Morton, R. J.; Vásquez, A. M. Bibcode: 2017A&A...603A.101L Altcode: 2017arXiv170310020L Context. EIT waves are freely-propagating global pulses in the low corona which are strongly associated with the initial evolution of coronal mass ejections (CMEs). They are thought to be large-amplitude, fast-mode magnetohydrodynamic waves initially driven by the rapid expansion of a CME in the low corona.
Aims: An EIT wave was observed on 6 July 2012 to impact an adjacent trans-equatorial loop system which then exhibited a decaying oscillation as it returned to rest. Observations of the loop oscillations were used to estimate the magnetic field strength of the loop system by studying the decaying oscillation of the loop, measuring the propagation of ubiquitous transverse waves in the loop and extrapolating the magnetic field from observed magnetograms.
Methods: Observations from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO/AIA) and the Coronal Multi-channel Polarimeter (CoMP) were used to study the event. An Empirical Mode Decomposition analysis was used to characterise the oscillation of the loop system in CoMP Doppler velocity and line width and in AIA intensity.
Results: The loop system was shown to oscillate in the 2nd harmonic mode rather than at the fundamental frequency, with the seismological analysis returning an estimated magnetic field strength of ≈ 5.5 ± 1.5 G. This compares to the magnetic field strength estimates of ≈1-9 G and ≈3-9 G found using the measurements of transverse wave propagation and magnetic field extrapolation respectively.

A movie associated to Figs. 1 and 2 is available at http://www.aanda.org Title: On-Disc Observations of Flux Rope Formation Prior to Its Eruption Authors: James, A. W.; Green, L. M.; Palmerio, E.; Valori, G.; Reid, H. A. S.; Baker, D.; Brooks, D. H.; van Driel-Gesztelyi, L.; Kilpua, E. K. J. Bibcode: 2017SoPh..292...71J Altcode: 2017arXiv170310837J Coronal mass ejections (CMEs) are one of the primary manifestations of solar activity and can drive severe space weather effects. Therefore, it is vital to work towards being able to predict their occurrence. However, many aspects of CME formation and eruption remain unclear, including whether magnetic flux ropes are present before the onset of eruption and the key mechanisms that cause CMEs to occur. In this work, the pre-eruptive coronal configuration of an active region that produced an interplanetary CME with a clear magnetic flux rope structure at 1 AU is studied. A forward-S sigmoid appears in extreme-ultraviolet (EUV) data two hours before the onset of the eruption (SOL2012-06-14), which is interpreted as a signature of a right-handed flux rope that formed prior to the eruption. Flare ribbons and EUV dimmings are used to infer the locations of the flux rope footpoints. These locations, together with observations of the global magnetic flux distribution, indicate that an interaction between newly emerged magnetic flux and pre-existing sunspot field in the days prior to the eruption may have enabled the coronal flux rope to form via tether-cutting-like reconnection. Composition analysis suggests that the flux rope had a coronal plasma composition, supporting our interpretation that the flux rope formed via magnetic reconnection in the corona. Once formed, the flux rope remained stable for two hours before erupting as a CME. Title: Analysis and modelling of recurrent solar flares observed with Hinode/EIS on March 9, 2012 Authors: Polito, V.; Del Zanna, G.; Valori, G.; Pariat, E.; Mason, H. E.; Dudík, J.; Janvier, M. Bibcode: 2017A&A...601A..39P Altcode: 2016arXiv161203504P Three homologous C-class flares and one last M-class flare were observed by both the Solar Dynamics Observatory (SDO) and the Hinode EUV Imaging Spectrometer (EIS) in the AR 11429 on March 9, 2012. All the recurrent flares occurred within a short interval of time (less than 4 h), showed very similar plasma morphology and were all confined, until the last one when a large-scale eruption occurred. The C-class flares are characterized by the appearance, at approximatively the same locations, of two bright and compact footpoint sources of ≈3-10 MK evaporating plasma, and a semi-circular ribbon. During all the flares, the continuous brightening of a spine-like hot plasma (≈10 MK) structure is also observed. Spectroscopic observations with Hinode/EIS are used to measure and compare the blueshift velocities in the Fe xxiii emission line and the electron number density at the flare footpoints for each flare. Similar velocities, of the order of 150-200 km s-1, are observed during the C2.0 and C4.7 confined flares, in agreement with the values reported by other authors in the study of the last M1.8 class flare. On the other hand, lower electron number densities and temperatures tend to be observed in flares with lower peak soft X-ray flux. In order to investigate the homologous nature of the flares, we performed a non-linear force-free field (NLFFF) extrapolation of the 3D magnetic field configuration in the corona. The NLFFF extrapolation and the Quasi-Separatrix Layers (QSLs) provide the magnetic field context which explains the location of the kernels, spine-like hot plasma and semi-circular brightenings observed in the (non-eruptive) flares. Given the absence of a coronal null point, we argue that the homologous flares were all generated by the continuous recurrence of bald patch reconnection.

The movie associated to Fig. 2 is available at http://www.aanda.org Title: Relative magnetic helicity as a diagnostic of solar eruptivity Authors: Pariat, E.; Leake, J. E.; Valori, G.; Linton, M. G.; Zuccarello, F. P.; Dalmasse, K. Bibcode: 2017A&A...601A.125P Altcode: 2017arXiv170310562P Context. The discovery of clear criteria that can deterministically describe the eruptive state of a solar active region would lead to major improvements on space weather predictions.
Aims: Using series of numerical simulations of the emergence of a magnetic flux rope in a magnetized coronal, leading either to eruptions or to stable configurations, we test several global scalar quantities for the ability to discriminate between the eruptive and the non-eruptive simulations.
Methods: From the magnetic field generated by the three-dimensional magnetohydrodynamical simulations, we compute and analyze the evolution of the magnetic flux, of the magnetic energy and its decomposition into potential and free energies, and of the relative magnetic helicity and its decomposition.
Results: Unlike the magnetic flux and magnetic energies, magnetic helicities are able to markedly distinguish the eruptive from the non-eruptive simulations. We find that the ratio of the magnetic helicity of the current-carrying magnetic field to the total relative helicity presents the highest values for the eruptive simulations, in the pre-eruptive phase only. We observe that the eruptive simulations do not possess the highest value of total magnetic helicity.
Conclusions: In the framework of our numerical study, the magnetic energies and the total relative helicity do not correspond to good eruptivity proxies. Our study highlights that the ratio of magnetic helicities diagnoses very clearly the eruptive potential of our parametric simulations. Our study shows that magnetic-helicity-based quantities may be very efficient for the prediction of solar eruptions. Title: Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method Authors: Guo, Y.; Pariat, E.; Valori, G.; Anfinogentov, S.; Chen, F.; Georgoulis, M. K.; Liu, Y.; Moraitis, K.; Thalmann, J. K.; Yang, S. Bibcode: 2017ApJ...840...40G Altcode: 2017arXiv170402096G We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov-Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger-Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field. Title: Magnetic helicity estimations in models and observations of the solar magnetic field Authors: Valori, Gherardo; Pariat, Etienne; Anfinogentov, Sergey; Chen, Feng; Georgoulis, Manolis; Guo, Yang; Liu, Yang; Moraitis, Kostas; Thalmann, Julia K.; Yang, Shangbin Bibcode: 2017EGUGA..19.3692V Altcode: Magnetic helicity, as one of the few conserved quantities in magneto-hydrodynamics, is often invoked as the principle driving the generation and structuring of magnetic fields in a variety of environments, from dynamo models in stars and planets, to post-disruption reconfigurations of tokamak's plasmas. Most particularly magnetic helicity has raised the interest of solar physicists, since helicity is suspected to represent a key quantity for the understanding of solar flares and the generation of coronal mass ejections. In recent years, several methods of estimation of magnetic helicity have been proposed and already applied to observations and numerical simulations. However, no systematic comparison of accuracy, mutual consistency, and reliability of such methods has ever been performed. We present the results of the first benchmark of several finite-volume methods in estimating magnetic helicity in 3D test models. In addition to finite volume methods, two additional methods are also included that estimate magnetic helicity based either on the field line's twist, or on the field's values on one boundary and an inferred minimal volume connectivity. The employed model tests range from solutions of the force-free equations to 3D magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of input fields. Our benchmark of finite volume methods allows to determine the reliability and precision of estimations of magnetic helicity in practical cases. As a next step, finite volume methods are used to test estimation methods that are based on the flux of helicity through one boundary, in particular for applications to observation-based models of coronal magnetic fields. The ultimate goal is to assess if and how can helicity be meaningfully used as a diagnostic of the evolution of magnetic fields in the solar atmosphere. Title: Determining the Intrinsic CME Flux Rope Type Using Remote-sensing Solar Disk Observations Authors: Palmerio, E.; Kilpua, E. K. J.; James, A. W.; Green, L. M.; Pomoell, J.; Isavnin, A.; Valori, G. Bibcode: 2017SoPh..292...39P Altcode: 2017arXiv170108595P A key aim in space weather research is to be able to use remote-sensing observations of the solar atmosphere to extend the lead time of predicting the geoeffectiveness of a coronal mass ejection (CME). In order to achieve this, the magnetic structure of the CME as it leaves the Sun must be known. In this article we address this issue by developing a method to determine the intrinsic flux rope type of a CME solely from solar disk observations. We use several well-known proxies for the magnetic helicity sign, the axis orientation, and the axial magnetic field direction to predict the magnetic structure of the interplanetary flux rope. We present two case studies: the 2 June 2011 and the 14 June 2012 CMEs. Both of these events erupted from an active region, and despite having clear in situ counterparts, their eruption characteristics were relatively complex. The first event was associated with an active region filament that erupted in two stages, while for the other event the eruption originated from a relatively high coronal altitude and the source region did not feature a filament. Our magnetic helicity sign proxies include the analysis of magnetic tongues, soft X-ray and/or extreme-ultraviolet sigmoids, coronal arcade skew, filament emission and absorption threads, and filament rotation. Since the inclination of the post-eruption arcades was not clear, we use the tilt of the polarity inversion line to determine the flux rope axis orientation and coronal dimmings to determine the flux rope footpoints, and therefore, the direction of the axial magnetic field. The comparison of the estimated intrinsic flux rope structure to in situ observations at the Lagrangian point L1 indicated a good agreement with the predictions. Our results highlight the flux rope type determination techniques that are particularly useful for active region eruptions, where most geoeffective CMEs originate. Title: <p>Prediction of In-Situ Magnetic Structure of Flux Ropes from Coronal Observations. Authors: Palmerio, E.; Kilpua, E.; James, A.; Green, L.; Pomoell, J.; Isavnin, A.; Valori, G.; Lumme, E. Bibcode: 2016AGUFMSH14A..03P Altcode: Coronal mass ejections (CMEs) are believed to be the main drivers of intense magnetic storms and various space weather phenomena at Earth. The most important parameter that defines the ability of a CME to drive geomagnetic storms is the north-south magnetic field component. One of the most significant problems in current long-term space weather forecasts is that there is no method to directly measure the magnetic structure of CMEs before they are observed in situ. In recent years, CMEs have been successfully modeled as unstable expanding flux ropes originating from low-corona, force-free flux equilibria (either containing or forming a flux rope in the wake of the instability). Due to their influence on the coronal plasma environment, the magnetic structure of CME flux ropes can be indirectly estimated based on the properties of the source active region and characteristics of the nearby structures, such as filament details, coronal EUV arcades and X-ray sigmoids. We present here a study of two CME flux ropes, aiming at determining their magnetic properties (magnetic helicity sign, flux rope tilt, and direction of the flux rope axial field) when launched from the Sun by using a synthesis of indirect proxies based on multi-wavelength remote sensing observations. In addition, we employ a data-driven magnetofrictional method that models the CME initiation in the corona to determine the magnetic structure in the two case studies. Finally, the predictions given by the observational synthesis and coronal modeling are compared with the structure detected in situ at Earth. Title: Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods Authors: Valori, Gherardo; Pariat, Etienne; Anfinogentov, Sergey; Chen, Feng; Georgoulis, Manolis K.; Guo, Yang; Liu, Yang; Moraitis, Kostas; Thalmann, Julia K.; Yang, Shangbin Bibcode: 2016SSRv..201..147V Altcode: 2016SSRv..tmp...68V; 2016arXiv161002193V Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3 %, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution. Title: Measuring the magnetic field of a trans-equatorial loop system using coronal seismology Authors: Long, David M.; Pérez-Suárez; D.; Valori; G. Bibcode: 2016usc..confE..25L Altcode: First observed by SOHO/EIT, "EIT waves" are strongly associated with the initial evolution of coronal mass ejections (CMEs) and after almost 20 years of investigation a consensus is being reached which interprets them as freely-propagating waves produced by the rapid expansion of a CME in the low corona. An "EIT wave" was observed on 6 July 2012 to erupt from active region AR11514 into a particularly structured corona that included multiple adjacent active regions as well as an adjacent trans-equatorial loop system anchored at the boundary of a nearby coronal hole. The eruption was well observed by SDO/AIA and CoMP, allowing the effects of the "EIT wave" on the trans-equatorial loop system to be studied in detail. In particular, it was possible to characterise the oscillation of the loop system using Doppler velocity measurements from CoMP. These Doppler measurements were used to estimate the magnetic field strength of the trans-equatorial loop system via coronal seismology. It was then possible to compare these inferred magnetic field values with both extrapolated magnetic field values from a Potential Field Source Surface extrapolation as well as the direct measurements of magnetic field provided by CoMP. These results show that the magnetic field strength of loop systems in the solar corona may be estimated using loop seismology. Title: Prediction of in-situ magnetic structure of flux ropes from coronal observations Authors: Palmerio, Erika; Kilpua, Emilia K. J.; Pomoell, Jens; James, Alexander; Green, Lucie M.; Isavnin, Alexey; Valori, Gherardo; Lumme, Erkka Bibcode: 2016usc..confE..33P Altcode: Coronal Mass Ejections (CMEs) are built at the Sun as nearly force-free (J x B = 0) magnetic flux ropes. It is well-established that CMEs are the main drivers of intense magnetic storms and various space weather phenomena at Earth. The most important parameter that defines the ability of a CME to drive geomagnetic storms is the north-south magnetic field component. One of the most significant problems in current long-term space weather forecasts is that there is no method to directly measure the magnetic structure of CMEs before they are observed in situ. However, due to their influence on the coronal plasma environment, the magnetic structure of CME flux ropes can be indirectly estimated based on the properties of the source active region and characteristics of the nearby structures, such as filament details, coronal EUV arcades and X-ray sigmoids. We present here a study of two CME flux ropes, aiming at determining their magnetic properties (magnetic helicity sign, flux rope tilt, and direction of the flux rope axial field) when launched from the Sun by using a synthesis of indirect proxies based on multi-wavelength remote sensing observations. In addition, we employ a data-driven magnetofrictional method that models the CME initiation in the corona to determine the magnetic structure in the two case studies. Finally, the predictions given by the observational synthesis and coronal modeling are compared with the structure detected in situ at Earth. Title: Magneto-frictional Modeling of Coronal Nonlinear Force-free Fields. I. Testing with Analytic Solutions Authors: Guo, Y.; Xia, C.; Keppens, R.; Valori, G. Bibcode: 2016ApJ...828...82G Altcode: We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov-Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax-Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper. Title: Flux Cancellation and the Evolution of the Eruptive Filament of 2011 June 7 Authors: Yardley, S. L.; Green, L. M.; Williams, D. R.; van Driel-Gesztelyi, L.; Valori, G.; Dacie, S. Bibcode: 2016ApJ...827..151Y Altcode: 2016arXiv160608264Y We investigate whether flux cancellation is responsible for the formation of a very massive filament resulting in the spectacular eruption on 2011 June 7. We analyze and quantify the amount of flux cancellation that occurs in NOAA AR 11226 and its two neighboring active regions (ARs 11227 & 11233) using line-of-sight magnetograms from the Heliospheric Magnetic Imager. During a 3.6 day period building up to the eruption of the filament, 1.7 × 1021 Mx, 21% of AR 11226's maximum magnetic flux, was canceled along the polarity inversion line (PIL) where the filament formed. If the flux cancellation continued at the same rate up until the eruption then up to 2.8 × 1021 Mx (34% of the AR flux) may have been built into the magnetic configuration that contains the filament plasma. The large flux cancellation rate is due to an unusual motion of the positive-polarity sunspot, which splits, with the largest section moving rapidly toward the PIL. This motion compresses the negative polarity and leads to the formation of an orphan penumbra where one end of the filament is rooted. Dense plasma threads above the orphan penumbra build into the filament, extending its length, and presumably injecting material into it. We conclude that the exceptionally strong flux cancellation in AR 11226 played a significant role in the formation of its unusually massive filament. In addition, the presence and coherent evolution of bald patches in the vector magnetic field along the PIL suggest that the magnetic field configuration supporting the filament material is that of a flux rope. Title: Photospheric Vector Magnetic Field Evolution of NOAA Active Region 11504 and the Ensuing CME Authors: James, Alexander; Green, Lucie; Valori, Gherardo; van Driel-Gesztelyi, Lidia; Baker, Deborah; Brooks, David; Palmerio, Erika Bibcode: 2016SPD....4730305J Altcode: Coronal mass ejections (CMEs) are eruptions of billions of tonnes of plasma from the Sun that drive the most severe space weather effects we observe. In order to be able to produce forecasts of space weather with lead times of the order of days, accurate predictions of the occurrence of CMEs must be developed. The eruptive active-region studied in this work (NOAA 11504) is complex, featuring fragmentation of penumbral magnetic field in the days prior to eruption, as well as rotation of the leading sunspot. SDO/HMI vector photospheric magnetic field measurements are utilised alongside SDO/AIA multi-wavelength extreme ultra-violet (EUV) observations to study the dynamics of the photospheric and coronal structures, as well as Hinode/EIS spectroscopic measurements, including elemental composition data. The EUV data show flare ribbons as well as coronal dimmings, which are used to infer the orientation of the erupting flux rope. This flux rope orientation is then compared to in situ measurements of the flux rope. The vector magnetic field data is used to determine the possible contributions the field fragmentation and sunspot rotation may have made to the formation of the flux rope and the triggering of the CME. Title: Measuring the magnetic field of a trans-equatorial loop system using coronal seismology Authors: Long, David; Perez-Suarez, David; Valori, Gherardo Bibcode: 2016SPD....47.0319L Altcode: First observed by SOHO/EIT, "EIT waves" are strongly associated with the initial evolution of coronal mass ejections (CMEs) and after almost 20 years of investigation a consensus is being reached which interprets them as freely-propagating waves produced by the rapid expansion of a CME in the low corona. An "EIT wave" was observed on 6 July 2012 to erupt from active region AR11514 into a particularly structured corona that included multiple adjacent active regions as well as an adjacent trans-equatorial loop system anchored at the boundary of a nearby coronal hole. The eruption was well observed by SDO/AIA and CoMP, allowing the effects of the "EIT wave" on the trans-equatorial loop system to be studied in detail. In particular, it was possible to characterise the oscillation of the loop system using Doppler velocity measurements from CoMP. These Doppler measurements were used to estimate the magnetic field strength of the trans-equatorial loop system via coronal seismology. It was then possible to compare these inferred magnetic field values with extrapolated magnetic field values derived using a Potential Field Source Surface extrapolation as well as the direct measurements of magnetic field provided by CoMP. These results show that the magnetic field strength of loop systems in the solar corona may be estimated using loop seismology. Title: Anomalous transmission of a coronal "EIT wave" through a nearby coronal hole Authors: Long, David; Perez-Suarez, David; Valori, Gherardo Bibcode: 2016SPD....47.0320L Altcode: Observations of reflection at coronal hole boundaries and transmission through the coronal hole suggest that "EIT waves" may be interpreted as freely--propagating wave--pulses initially driven by the rapid expansion of a coronal mass ejection (CME) in the low corona. An "EIT wave" observed on 2012 July 07 is seen to impact an adjacent coronal hole. However, rather than reappearing at the far edge of the coronal hole as with previous observations, the "EIT wave" was subsequently observed to reappear ~360 Mm away in the quiet Sun. The non-typical evolution of the "EIT wave" is examined using a combination of observations of the eruption from SDO/AIA and STEREO-A/EUVI as well as extrapolations of the global magnetic field. The observed "jump" in position of the "EIT wave" is shown to be due to the wave pulse traveling along hot coronal loops connecting the edge of the coronal hole with the quiet Sun. Title: Tracking the magnetic structure of flux ropes from eruption to in-situ detection Authors: Palmerio, Erika; Kilpua, Emilia; Green, Lucie; James, Alexander; Pomoell, Jens; Valori, Gherardo Bibcode: 2016EGUGA..18.1641P Altcode: Coronal Mass Ejections (CMEs) are spectacular explosions from the Sun where huge amounts of plasma and magnetic flux are ejected into the heliosphere. CMEs are built at the Sun as a force-free (J ×B = 0) magnetic flux rope. It is well-established that CMEs are the main drivers of intense magnetic storms and various space weather effects at the Earth. One of the most significant problems for improving the long lead-time space weather predictions is that there is no method to directly measure the structure of CME magnetic fields, neither in the onset process nor during the subsequent propagation from the solar surface to the Earth. The magnetic properties of the CME flux rope (magnetic helicity sign, the flux rope tilt and the direction of the flux rope axial field) can be estimated based on the properties of the source active region and characteristics of the related structures, such as filament details, coronal EUV arcades and X-ray sigmoids. We present here a study of two CME flux ropes. We compare their magnetic structure using the synthesis of these indirect proxies based on multi-wavelength remote sensing observations with the structure detected in-situ near the orbit of the Earth. Title: Restricted propagation of an ``EIT wave'' in the low solar corona Authors: Long, David M.; Pérez-Suárez, David; Valori, Gherardo Bibcode: 2016IAUS..320...98L Altcode: We present observations of an ``EIT wave'' associated with an X-class flare from 2012 July 6, the propagation of which was severely restricted by the magnetic structure of the solar corona surrounding the erupting active region. The ``EIT wave'' was observed by both SDO and STEREO-A, allowing a three-dimensional examination of how the propagation of the disturbance was affected both by a neighbouring coronal hole and a trans-equatorial loop system. In addition, the eruption was observed at the limb by the ground-based CoMP instrument, allowing the Doppler motion associated with the eruption and resulting coronal loop oscillation to be investigated in detail. This combination of data-sets provides a unique insight into the three-dimensional evolution of the ``EIT wave'' and its effects on the surrounding corona. Title: The Influence of Spatial resolution on Nonlinear Force-free Modeling Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.; Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori, G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.; Régnier, S. Bibcode: 2015ApJ...811..107D Altcode: 2015arXiv150805455D 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/Solar Optical Telescope Spectro-Polarimeter 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. Title: Testing magnetic helicity conservation in a solar-like active event Authors: Pariat, E.; Valori, G.; Démoulin, P.; Dalmasse, K. Bibcode: 2015A&A...580A.128P Altcode: 2015arXiv150609013P Context. Magnetic helicity has the remarkable property of being a conserved quantity of ideal magnetohydrodynamics (MHD). Therefore, it could be used as an effective tracer of the magnetic field evolution of magnetized plasmas.
Aims: Theoretical estimations indicate that magnetic helicity is also essentially conserved with non-ideal MHD processes, for example, magnetic reconnection. This conjecture has been barely tested, however, either experimentally or numerically. Thanks to recent advances in magnetic helicity estimation methods, it is now possible to numerically test its dissipation level in general three-dimensional datasets.
Methods: We first revisit the general formulation of the temporal variation of relative magnetic helicity on a fully bounded volume when no hypothesis on the gauge is made. We introduce a method for precisely estimating its dissipation independently of which type of non-ideal MHD processes occurs. For a solar-like eruptive-event simulation, using different gauges, we compare an estimate of the relative magnetic helicity computed in a finite volume with its time-integrated flux through the boundaries. We thus test the conservation and dissipation of helicity.
Results: We provide an upper bound of the real dissipation of magnetic helicity: It is quasi-null during the quasi-ideal MHD phase. Even with magnetic reconnection, the relative dissipation of magnetic helicity is also very low (<2.2%), in particular compared to the relative dissipation of magnetic energy (>30 times higher). We finally illustrate how the helicity-flux terms involving velocity components are gauge dependent, which limits their physical meaning.
Conclusions: Our study paves the way for more extended and diverse tests of the magnetic helicity conservation properties. Our study confirms the central role of helicity in the study of MHD plasmas. For instance, the conservation of helicity can be used to track the evolution of solar magnetic fields from when they form in the solar interior until their detection as magnetic clouds in the interplanetary space.

Appendix A is available in electronic form at http://www.aanda.org Title: Time Evolution of Force-Free Parameter and Free Magnetic Energy in Active Region NOAA 10365 Authors: Valori, G.; Romano, P.; Malanushenko, A.; Ermolli, I.; Giorgi, F.; Steed, K.; van Driel-Gesztelyi, L.; Zuccarello, F.; Malherbe, J. -M. Bibcode: 2015SoPh..290..491V Altcode: We describe the variation of the accumulated coronal helicity derived from the magnetic helicity flux through the photosphere in active region (AR) NOAA 10365, where several large flares and coronal mass ejections (CMEs) occurred. We used SOHO/MDI full-disk line-of-sight magnetograms to measure the helicity flux, and the integral of GOES X-ray flux as a proxy of the coronal energy variations due to flares or CMEs. Using the linear force-free field model, we transformed the accumulated helicity flux into a time sequence of the force-free parameter α accounting for flares or CMEs via the proxy derived from GOES observations. This method can be used to derive the value of α at different times during the AR evolution, and is a partial alternative to the commonly used match of field lines with EUV loops. By combining the accumulated helicity obtained from the observations with the linear force-free theory, we describe the main phases of the emergence process of the AR, and relate them temporally with the occurrence of flares or CMEs. Additionally, a comparison with the loop-matching method of fixing alpha at each time independently shows that the proposed method may be helpful in avoiding unrealistic or undetermined values of alpha that may originate from an insufficient quality of the image used to identify coronal loops at a given time. For the relative intensity of the considered events, the linear force-free field theory implies that there is a direct correlation between the released energy on the one hand and the product of the coronal helicity with the variation of α due to the event on the other. Therefore, the higher the value of the accumulated coronal helicity, the smaller the force-free parameter variation required to produce the same decrease in the free energy during the CMEs. Title: Coronal Magnetic Reconnection Driven by CME Expansion—the 2011 June 7 Event Authors: van Driel-Gesztelyi, L.; Baker, D.; Török, T.; Pariat, E.; Green, L. M.; Williams, D. R.; Carlyle, J.; Valori, G.; Démoulin, P.; Kliem, B.; Long, D. M.; Matthews, S. A.; Malherbe, J. -M. Bibcode: 2014ApJ...788...85V Altcode: 2014arXiv1406.3153V Coronal mass ejections (CMEs) erupt and expand in a magnetically structured solar corona. Various indirect observational pieces of evidence have shown that the magnetic field of CMEs reconnects with surrounding magnetic fields, forming, e.g., dimming regions distant from the CME source regions. Analyzing Solar Dynamics Observatory (SDO) observations of the eruption from AR 11226 on 2011 June 7, we present the first direct evidence of coronal magnetic reconnection between the fields of two adjacent active regions during a CME. The observations are presented jointly with a data-constrained numerical simulation, demonstrating the formation/intensification of current sheets along a hyperbolic flux tube at the interface between the CME and the neighboring AR 11227. Reconnection resulted in the formation of new magnetic connections between the erupting magnetic structure from AR 11226 and the neighboring active region AR 11227 about 200 Mm from the eruption site. The onset of reconnection first becomes apparent in the SDO/AIA images when filament plasma, originally contained within the erupting flux rope, is redirected toward remote areas in AR 11227, tracing the change of large-scale magnetic connectivity. The location of the coronal reconnection region becomes bright and directly observable at SDO/AIA wavelengths, owing to the presence of down-flowing cool, dense (1010 cm-3) filament plasma in its vicinity. The high-density plasma around the reconnection region is heated to coronal temperatures, presumably by slow-mode shocks and Coulomb collisions. These results provide the first direct observational evidence that CMEs reconnect with surrounding magnetic structures, leading to a large-scale reconfiguration of the coronal magnetic field. Title: Constraining magnetic flux emergence from a timeseries of helicitigrams Authors: Dalmasse, Kévin; Pariat, Etienne; Green, Lucie M.; Aulanier, Guillaume; Demoulin, Pascal; Valori, Gherardo Bibcode: 2014cosp...40E.612D Altcode: Magnetic helicity quantifies how globally twisted and/or sheared is the magnetic field in a volume. Observational studies have reported the injection of large amounts of magnetic helicity associated with the emergence of magnetic flux into the solar atmosphere. Because magnetic helicity is conserved in the convection zone, the injection of magnetic helicity into the solar corona reflects the helicity content of emerging magnetic flux tubes. Mapping the photospheric injection of magnetic helicity thus seems to be a key tool for constraining the parameters of the emerging flux tubes in numerical case-studies of observed active regions. We recently developed a method to compute the distribution of magnetic helicity flux. Contrary to previous proxies, this method takes into account the 3D nature of magnetic helicity, and is thus, better-suited to study the distribution of helicity flux. After introducing this method, we will present the results of its application to the NOAA AR 11158. We will show that, the distribution of helicity flux is complex, with patterns of real mixed signals of helicity flux related to the specific topology of the active region's magnetic field. Finally, we will discuss the implications of our results on the evolution and dynamics of this active region. Title: Magnetic reconnection driven by filament eruption in the 7 June 2011 event Authors: van Driel-Gesztelyi, L.; Baker, D.; Török, T.; Pariat, E.; Green, L. M.; Williams, D. R.; Carlyle, J.; Valori, G.; Démoulin, P.; Matthews, S. A.; Kliem, B.; Malherbe, J. -M. Bibcode: 2014IAUS..300..502V Altcode: During an unusually massive filament eruption on 7 June 2011, SDO/AIA imaged for the first time significant EUV emission around a magnetic reconnection region in the solar corona. The reconnection occurred between magnetic fields of the laterally expanding CME and a neighbouring active region. A pre-existing quasi-separatrix layer was activated in the process. This scenario is supported by data-constrained numerical simulations of the eruption. Observations show that dense cool filament plasma was re-directed and heated in situ, producing coronal-temperature emission around the reconnection region. These results provide the first direct observational evidence, supported by MHD simulations and magnetic modelling, that a large-scale re-configuration of the coronal magnetic field takes place during solar eruptions via the process of magnetic reconnection. Title: Initiation of Coronal Mass Ejections by Sunspot Rotation Authors: Valori, G.; Török, T.; Temmer, M.; Veronig, A. M.; van Driel-Gesztelyi, L.; Vršnak, B. Bibcode: 2014IAUS..300..201V Altcode: We report observations of a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in Active Region NOAA 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux rope, using three-dimensional zero-β MHD simulations. We consider a magnetic configuration whose photospheric flux distribution and coronal structure is guided by the observations and a potential field extrapolation. We find that the twisting leads to the expansion of the overlying field. As a consequence of the progressively reduced magnetic tension, the flux rope quasi-statically adapts to the changed environmental field, rising slowly. Once the tension is sufficiently reduced, a distinct second phase of evolution occurs where the flux rope enters an unstable regime characterized by a strong acceleration. Our simulation thus suggests a new mechanism for the triggering of eruptions in the vicinity of rotating sunspots. Title: Initiation of Coronal Mass Ejections by Sunspot Rotation Authors: Török, T.; Temmer, M.; Valori, G.; Veronig, A. M.; van Driel-Gesztelyi, L.; Vršnak, B. Bibcode: 2013SoPh..286..453T Altcode: 2014arXiv1401.2922T We study a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in NOAA Active Region 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux-rope, using three-dimensional zero-β MHD simulations. We first consider a relatively simple and symmetric system, and then study a more complex and asymmetric magnetic configuration, whose photospheric-flux distribution and coronal structure are guided by the observations and a potential field extrapolation. In both cases, we find that the twisting leads to the expansion of the overlying field. As a consequence of the progressively reduced magnetic tension, the flux-rope quasi-statically adapts to the changed environmental field, rising slowly. Once the tension is sufficiently reduced, a distinct second phase of evolution occurs where the flux-rope enters an unstable regime characterised by a strong acceleration. Our simulations thus suggest a new mechanism for the triggering of eruptions in the vicinity of rotating sunspots. Title: First observational application of a connectivity-based helicity flux density Authors: Dalmasse, K.; Pariat, E.; Valori, G.; Démoulin, P.; Green, L. M. Bibcode: 2013A&A...555L...6D Altcode: 2013arXiv1307.2838D Context. Measuring the magnetic helicity distribution in the solar corona can help in understanding the trigger of solar eruptive events because magnetic helicity is believed to play a key role in solar activity due to its conservation property.
Aims: A new method for computing the photospheric distribution of the helicity flux was recently developed. This method takes into account the magnetic field connectivity whereas previous methods were based on photospheric signatures only. This novel method maps the true injection of magnetic helicity in active regions. We applied this method for the first time to an observed active region, NOAA 11158, which was the source of intense flaring activity.
Methods: We used high-resolution vector magnetograms from the SDO/HMI instrument to compute the photospheric flux transport velocities and to perform a nonlinear force-free magnetic field extrapolation. We determined and compared the magnetic helicity flux distribution using a purely photospheric as well as a connectivity-based method.
Results: While the new connectivity-based method confirms the mixed pattern of the helicity flux in NOAA 11158, it also reveals a different, and more correct, distribution of the helicity injection. This distribution can be important for explaining the likelihood of an eruption from the active region.
Conclusions: The connectivity-based approach is a robust method for computing the magnetic helicity flux, which can be used to study the link between magnetic helicity and eruptivity of observed active regions. Title: Accuracy of magnetic energy computations Authors: Valori, G.; Démoulin, P.; Pariat, E.; Masson, S. Bibcode: 2013A&A...553A..38V Altcode: 2013arXiv1303.6773V Context. For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, 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. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional (3D) models of the solar atmosphere, e.g., in coronal fields reconstructions or numerical simulations.
Aims: The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration.
Methods: We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used.
Results: The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component of the field. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence.
Conclusions: We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources. We also compare the efficiency of two divergence-cleaning techniques. These results are applicable to a broad range of numerical realizations of magnetic fields.

Appendices are available in electronic form at http://www.aanda.org Title: Comparing Values of the Relative Magnetic Helicity in Finite Volumes Authors: Valori, G.; Démoulin, P.; Pariat, E. Bibcode: 2012SoPh..278..347V Altcode: 2012SoPh..tmp..271G Relative magnetic helicity, as a conserved quantity of ideal magnetohydrodynamics, has been highlighted as an important quantity to study in plasma physics. Due to its nonlocal nature, its estimation is not straightforward in both observational and numerical data. In this study we derive expressions for the practical computation of the gauge-independent relative magnetic helicity in three-dimensional finite domains. The derived expressions are easy to implement and rapid to compute. They are derived in Cartesian coordinates, but can be easily written in other coordinate systems. We apply our method to a numerical model of a force-free equilibrium containing a flux rope, and compare the results with those obtained employing known half-space equations. We find that our method requires a much smaller volume than half-space expressions to derive the full helicity content. We also prove that values of relative magnetic helicity of different magnetic fields can be compared with each other in the same sense as free-energy values can. Therefore, relative magnetic helicity can be meaningfully and directly compared between different datasets, such as those from different active regions, but also within the same dataset at different times. Typical applications of our formulae include the helicity computation in three-dimensional models of the solar atmosphere, e.g., coronal-field reconstructions by force-free extrapolation and discretized magnetic fields of numerical simulations. Title: Nonlinear Force-Free Extrapolation of Emerging Flux with a Global Twist and Serpentine Fine Structures Authors: Valori, G.; Green, L. M.; Démoulin, P.; Vargas Domínguez, S.; van Driel-Gesztelyi, L.; Wallace, A.; Baker, D.; Fuhrmann, M. Bibcode: 2012SoPh..278...73V Altcode: We study the flux emergence process in NOAA active region 11024, between 29 June and 7 July 2009, by means of multi-wavelength observations and nonlinear force-free extrapolation. The main aim is to extend previous investigations by combining, as much as possible, high spatial resolution observations to test our present understanding of small-scale (undulatory) flux emergence, whilst putting these small-scale events in the context of the global evolution of the active region. The combination of these techniques allows us to follow the whole process, from the first appearance of the bipolar axial field on the east limb, until the buoyancy instability could set in and raise the main body of the twisted flux tube through the photosphere, forming magnetic tongues and signatures of serpentine field, until the simplification of the magnetic structure into a main bipole by the time the active region reaches the west limb. At the crucial time of the main emergence phase high spatial resolution spectropolarimetric measurements of the photospheric field are employed to reconstruct the three-dimensional structure of the nonlinear force-free coronal field, which is then used to test the current understanding of flux emergence processes. In particular, knowledge of the coronal connectivity confirms the identity of the magnetic tongues as seen in their photospheric signatures, and it exemplifies how the twisted flux, which is emerging on small scales in the form of a sea-serpent, is subsequently rearranged by reconnection into the large-scale field of the active region. In this way, the multi-wavelength observations combined with a nonlinear force-free extrapolation provide a coherent picture of the emergence process of small-scale magnetic bipoles, which subsequently reconnect to form a large-scale structure in the corona. Title: A comparison of preprocessing methods for solar force-free magnetic field extrapolation Authors: Fuhrmann, M.; Seehafer, N.; Valori, G.; Wiegelmann, T. Bibcode: 2011A&A...526A..70F Altcode: 2010arXiv1010.6015F Context. 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. This condition is violated in the photosphere itself and a thin layer in the lower atmosphere above. The field calculations can be improved by preprocessing the photospheric magnetograms. The intention here is to remove a non-force-free component from the data.
Aims: We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann et al. (2007, A&A, 476, 349).
Methods: The two preprocessing methods were applied to a vector magnetogram of the recently observed active region NOAA AR 10 953. 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.
Results: 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. The force and torque decrease is stronger for the Fuhrmann et al. method. 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. Title: Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions Authors: Valori, G.; Kliem, B.; Török, T.; Titov, V. S. Bibcode: 2010A&A...519A..44V Altcode: 2010arXiv1005.0254V We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Démoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version with a parabolic current density profile is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade - “hyperbolic flux tube” and “bald patch separatrix surface” - are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Démoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases, which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy. Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T. Bibcode: 2009SPD....40.3102D Altcode: Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models. Title: A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953 Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham; Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar; Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann, Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas; Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester, Bernd; Tadesse, Tilaye Bibcode: 2009ApJ...696.1780D Altcode: 2009arXiv0902.1007D 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 paper, 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 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. Title: Nonlinear Force-Free Magnetic Field Modeling of the Solar Corona: A Critical Assessment Authors: De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.; Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T. Bibcode: 2008AGUFMSH41A1604D Altcode: Nonlinear force-free field (NLFFF) modeling promises to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have so far failed to arrive at consistent solutions when applied to cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not been available). It is our view that the lack of robust results indicates an endemic problem with the NLFFF modeling process, and that this process will likely continue to fail until (1) more of the far-reaching, current-carrying connections are within the observational field of view, (2) the solution algorithms incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is found to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models. Title: Coronal Magnetic Field Extrapolation from Photospheric Measurements Applied to an Active Region Authors: Fuhrmann, M.; Kliem, B.; Valori, G.; Seehafer, N. Bibcode: 2008ESPM...12.3.37F Altcode: We outline an MHD relaxation method that permits to extrapolate photospheric vector magnetograms into coronal nonlinear force-free fields. The method is applied to a magnetogram taken before an eruptive event in NOAA AR 7792 on 25 October 1994. The event produced a coronal mass ejection (CME) and eruptive flare with a prominent sigmoidal soft X-ray source. Multiwavelength observations as well as theoretical modeling indicate the importance of twisted magnetic configurations in solar active regions(ARs) in the initiation of such events. Manoharan et al. (1996) proposed a model for this event that included the merging of two slightly twisted flux bundles near the polarity inversion line into a flux rope of larger total twist and an overlying flux system much closer to a potential-field state. For the extrapolation we use a vector magnetogram taken at the Mees Solar Observatory 16 hours before the actual event. The magnetic field extrapolation is able to recover main parts of the structures suggested in the model by Manoharan et al. We find the overlying nearly potential flux and part of the sigmoidal field, i.e., one of the suggested weakly twisted flux bundles, in the location observed. This supports the notion that sigmoids are coronal manifestations of twisted magnetic flux tubes which start expanding in eruptive events and may exist even before the onset of such events. We tentatively attribute the incomplete reconstruction of the sigmoidal field structure to the strong evolution of the photospheric field at the suggested location of flux tube merging between the time of the magnetogram and the eruption, as indicated by a magnetogram on the following day. Title: Magnetofrictional Extrapolations of Current-Carrying Flux Ropes Authors: Valori, G.; Kliem, B.; Toeroek, T. Bibcode: 2008ESPM...12.2.90V Altcode: The quiescent solar corona is regularly modified by very fast ejections of coronal material and magnetic field (CME) that occur preferably above active regions. Most CME models require the formation of twisted magnetic field structures (flux ropes) before or during such events.

Unfortunately, the coronal magnetic field is not directly measurable at present, and therefore it is difficult to verify the validity of different CME models.

In order to remove this obstacle, the extrapolation of photospheric magnetic field measurements can be used to reconstruct the missing coronal information. As an application of our magneto-frictional code, we present an extrapolation of a measured magnetogram where a flux rope is found.

In such applications it is necessary to estimate how well our extrapolation code can reproduce all aspects of highly nonlinear structures such as flux ropes. This is of course possible only using test fields.

The Titov and Demoulin force-free equilibrium (Titov and Demoulin, Astr. and Astrophys. 351, 707, (1999), hereafter TD) models a semi-circular, 3D current-carrying flux rope by means of a current ring embedded in a potential field. The parameters of the TD model can be adjusted to create both stable and kink- and torus-unstable configurations.

Its solar relevance was confirmed by the quantitative reproduction of some specific CME features (see e.g., Toeroek and Kliem, Astroph. J. Lett. 630 L97 (2005)).

Therefore, the TD solution is by far the most realistic analytical equilibrium available to date for the modeling of solar active regions.

Employing the TD equilibrium as a test-field, we show that the magnetofrictional extrapolation code can reproduce the energy and the twist of the magnetic field within a percent accuracy.

This information is essential for the reconstruction of coronal fields involved in eruptions because the twist is, together with the height profile of the overlying potential field, the most important stability parameter -- at least as long as the TD equilibrium is a good model of the considered active region.

Perfectly reproduced are also X-type magnetic topology features, sometimes referred to as Hyperbolic Flux Tubes, which are regarded to be essential to the physics of CMEs and flares because they are preferred locations for the formation of current sheets.

On the other hand, we also show how the scale-height of the potential field that is used as initial condition in the extrapolation influences the quality of the reconstructed field: different initial conditions reproduce correctly the twist and the topology, but less accurately the height and the shape of the flux rope.

Consequently, care must be taken when comparing the shapes of soft X-ray and EUV loops, especially those in the nearly potential field overlying filaments, with the field lines obtained from the extrapolation of the corresponding magnetogram. Title: Non-Linear Force-Free Field Modeling of a Solar Active Region Around the Time of a Major Flare and Coronal Mass Ejection Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. Bibcode: 2008AGUSMSP31A..06D Altcode: Solar flares and coronal mass ejections are associated with rapid changes in coronal magnetic field connectivity and are powered by the partial dissipation of electrical currents that run through the solar corona. A critical unanswered question is whether the currents involved are induced by the advection along the photosphere of pre-existing atmospheric magnetic flux, or whether these currents are associated with newly emergent flux. We address this problem by applying nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare in December 2006. We compute 14 NLFFF models using 4 different codes having a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We do find agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032~erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. We discuss the relative merits of these models in a general critique of our present abilities to model the coronal magnetic field based on surface vector field measurements. Title: Nonlinear Force-free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. K. Bibcode: 2008ApJ...675.1637S Altcode: 2007arXiv0712.0023S Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields Authors: Metcalf, Thomas R.; De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham; van Ballegooijen, Adriaan A.; Wiegelmann, Thomas; Wheatland, Michael S.; Valori, Gherardo; McTtiernan, James M. Bibcode: 2008SoPh..247..269M Altcode: 2008SoPh..tmp...17M We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad - Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced "photospheric" and more force-free "chromospheric" vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field's free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. Title: Force-free magnetic fields in the solar atmosphere Authors: Seehafer, N.; Fuhrmann, M.; Valori, G.; Kliem, B. Bibcode: 2007AN....328.1166S Altcode: Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. Title: Preprocessing of solar vector magnetograms for force-free magnetic field extrapolation Authors: Fuhrmann, M.; Seehafer, N.; Valori, G. Bibcode: 2007A&A...476..349F Altcode: Context: Reliable measurements of the solar magnetic field are restricted to the phoptosphere. As an alternative to measurements, the field in the higher layers of the atmosphere is calculated from the measured photospheric field, mostly under the assumption that it is force-free. However, the magnetic field in the photosphere is not force-free. Moreover, most methods for the extrapolation of the photospheric magnetic field into the higher layers prescribe the magnetic vector on the whole boundary of the considered volume, which overdetermines the force-free field. Finally, the extrapolation methods are very sensitive to small-scale noise in the magnetograph data, which, however, if sufficienly resolved numerically, should affect the solution only in a thin boundary layer close to the photosphere.
Aims: A new method for the preprocessing of solar photospheric vector magnetograms has been developed that, by improving their compatibility with the condition of force-freeness and removing small-scale noise, makes them more suitable for extrapolations into three-dimensional nonlinear force-free magnetic fields in the chromosphere and corona.
Methods: A functional of the photospheric field values is minimized whereby the total magnetic force and the total magnetic torque on the considered volume above the photosphere, as well as a quantity measuring the degree of small-scale noise in the photospheric boundary data, are simultaneously made small. For the minimization, the method of simulated annealing is used and the smoothing of noisy magnetograph data is attained by windowed median averaging.
Results: The method was applied to a magnetogram derived from a known nonlinear force-free test field to which an artificial noise had been added. The algorithm recovered all main structures of the magnetogram and removed small-scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram before and after the preprocessing. The preprocessing was found to significantly improve the agreement of the extrapolated with the exact field. Title: Magnetofrictional Extrapolations of Low and Lou's Force-Free Equilibria Authors: Valori, G.; Kliem, B.; Fuhrmann, M. Bibcode: 2007SoPh..245..263V Altcode: We present a careful investigation of the magnetofrictional relaxation and extrapolation technique applied to the reconstruction of two test fields. These fields are taken from the family of nonlinear force-free magnetic equilibria constructed by Low and Lou (Astrophys. J.352, 343, 1990), which have emerged as standard tests for extrapolation techniques in recent years. For the practically relevant case that only the field values in the bottom plane of the considered volume (vector magnetogram) are used as input information (i.e., not including the knowledge about the test field at the side and top boundaries), the test field is reconstructed to a higher accuracy than obtained previously. Detailed diagnostics of the reconstruction accuracy show that the implementation of fourth-order spatial discretization was essential to reach this accuracy for the given test fields and to achieve near machine precision in satisfying the solenoidal condition. Different variants of boundary conditions are tested, which all yield comparable accuracy. In its present implementation, the technique yields a scaling of computing time with total number of grid points only slightly below N5/3, which is too steep for applications to large (≥10242) magnetograms, except on supercomputers. Directions for improvement are outlined. Title: Non-linear Force-free Modeling Of Coronal Magnetic Fields Authors: Metcalf, Thomas R.; De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; van Ballegooijen, A.; Wiegelmann, T.; Wheatland, M. S.; Valori, G.; McTiernan, J. M. Bibcode: 2007AAS...210.9102M Altcode: 2007BAAS...39..204M We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad-Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced "photospheric'' and more force-free "chromospheric'' vector magnetic field boundary data derived from the model. When applied to the

chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field's free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the Lorentz forces on the photosphere severely impact the extrapolation of the field. Preprocessing of the photospheric boundary does improve the extrapolations considerably, although the results depend sensitively on the details of the numerical codes. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. Title: Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Démoulin equilibrium Authors: Wiegelmann, T.; Inhester, B.; Kliem, B.; Valori, G.; Neukirch, T. Bibcode: 2006A&A...453..737W Altcode: 2006astro.ph.12650W 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. Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part I: A Quantitative Comparison of Methods Authors: Schrijver, Carolus J.; De Rosa, Marc L.; Metcalf, Thomas R.; Liu, Yang; McTiernan, Jim; Régnier, Stéphane; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas Bibcode: 2006SoPh..235..161S Altcode: We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional, Grad-Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest. The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions; best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest. For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error En = « |B−b|»/« |B|» of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while the total energy in the magnetic field is approximated to within 2%. The models converge towards the central, strong input field at speeds that differ by a factor of one million per iteration step. The fastest-converging, best-performing model for these analytical test cases is the Wheatland, Sturrock, and Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann (2004). Title: Extrapolation of a nonlinear force-free field containing a highly twisted magnetic loop Authors: Valori, G.; Kliem, B.; Keppens, R. Bibcode: 2005A&A...433..335V Altcode: The stress-and-relax method for the extrapolation of nonlinear force-free coronal magnetic fields from photospheric vector magnetograms is formulated and implemented in a manner analogous to the evolutionary extrapolation method. The technique is applied to a numerically constructed force-free equilibrium that has a simple bipolar structure of the normal field component in the bottom (magnetogram) plane but contains a highly twisted loop and a shear (current) layer, with a smooth but strong variation of the force-free parameter α in the magnetogram. A standard linear force-free extrapolation of this magnetogram, using the so-called α_best value, is found to fail in reproducing the twisted loop (or flux rope) and the shear layer; it yields a loop pair instead and the shear is not concentrated in a layer. With the nonlinear extrapolation technique, the given equilibrium is readily reconstructed to a high degree of accuracy if the magnetogram is sufficiently resolved. A parametric study quantifies the requirements on the resolution for a successful nonlinear extrapolation. Permitting magnetic reconnection by a controlled use of resistivity improved the extrapolation at a resolution comparable to the smallest structures in the magnetogram. Title: Fluid and kinetic aspects of collisionless magnetic reconnection Authors: Valori, Gherardo Bibcode: 2001PhDT........99V Altcode: No abstract at ADS