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, , shows a strong ability to indicate the eruptive potential of a solar AR. However, 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, , represents no indicator for the eruptivity.
Context. The study of the magnetic topology of magnetic fields aims at determining the key sites for the development of magnetic reconnection. Quasi-separatrix layers (QSLs), regions of strong ...connectivity gradients, are topological structures where intense-electric currents preferentially build-up, and where, later on, magnetic reconnection occurs. Aims. QSLs are volumes of intense squashing degree, Q; the field-line invariant quantifying the deformation of elementary flux tubes. QSL are complex and thin three-dimensional (3D) structures difficult to visualize directly. Therefore Q maps, i.e. 2D cuts of the 3D magnetic domain, are a more and more common features used to study QSLs. Methods. We analyze several methods to derive 2D Q maps and discuss their analytical and numerical properties. These methods can also be used to compute Q within the 3D domain. Results. We demonstrate that while analytically equivalent, the numerical implementation of these methods can be significantly different. We derive the analytical formula and the best numerical methodology that should be used to compute Q inside the 3D domain. We illustrate this method with two twisted magnetic configurations: a theoretical case and a non-linear force free configuration derived from observations. Conclusions. The representation of QSL through 2D planar cuts is an efficient procedure to derive the geometry of these structures and to relate them with other quantities, e.g. electric currents and plasma flows. It will enforce a more direct comparison of the role of QSL in magnetic reconnection.
We present for the first time the evolution of the photospheric electric currents during an eruptive X-class flare, accurately predicted by the standard three-dimensional (3D) flare model. We analyze ...this evolution for the 2011 February 15 flare using Helioseismic and Magnetic Imager/Solar Dynamics Observatory magnetic observations and find that localized currents in J-shaped ribbons increase to double their pre-flare intensity. Our 3D flare model, developed with the OHM code, suggests that these current ribbons, which develop at the location of extreme ultraviolet brightenings seen with Atmospheric Imaging Assembly imagery, are driven by the collapse of the flare's coronal current layer. These findings of increased currents restricted in localized ribbons are consistent with the overall free energy decrease during a flare, and the shapes of these ribbons also give an indication of how twisted the erupting flux rope is. Finally, this study further enhances the close correspondence obtained between the theoretical predictions of the standard 3D model and flare observations, indicating that the main key physical elements are incorporated in the model.
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.
A standard model for eruptive flares aims at describing observational 3D features of the reconnecting coronal magnetic field. Extensions to the 20 model require the physical understanding of 3D ...reconnection processes at the origin of the magnetic configuration evolution. We focus on magnetic reconnection associated with the growth and evolution of a flux rope and associated flare loops during an eruptive flare. We aim at understanding the intrinsic characteristics of 3D reconnection in the presence of quasi-separatrix layers (QSLs), how QSL properties are related to the slip-running reconnection mode in general, and how this applies to eruptive flares in particular. The present analysis extends our understanding of the 3D slip-running reconnection regime. We identified a controlling parameter of the apparent velocity of field lines while they slip-reconnect, enabling the interpretation of the evolution of post flare loops. This work completes the standard model for flares and eruptions by giving its 3D properties.
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.
Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While ...the energy involved in a jet-like event is smaller than that of "nominal" solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the size-spectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solar-heliospheric problems.
Flare ribbons are commonly attributed to the low-altitude impact, along the footprints of separatrices or quasi-separatrix layers (QSLs), of particle beams accelerated through magnetic reconnection. ...If reconnection occurs at a three-dimensional coronal magnetic null point, the footprint of the dome-shaped fan surface would map a closed circular ribbon. This paper addresses the following issues: does the entire circular ribbon brighten simultaneously, as expected because all fan field lines pass through the null point? And since the spine separatrices are singular field lines, do spine-related ribbons look like compact kernels? What can we learn from these observations about current sheet formation and magnetic reconnection in a null-point topology? The present study addresses these questions by analyzing Transition Region and Coronal Explorer and Solar and Heliospheric Observatory/Michelson Doppler Imager observations of a confined flare presenting a circular ribbon. Using a potential field extrapolation, we linked the circular shape of the ribbon with the photospheric mapping of the fan field lines originating from a coronal null point. Observations show that the flare ribbon outlining the fan lines brightens sequentially along the counterclockwise direction and that the spine-related ribbons are elongated. Using the potential field extrapolation as initial condition, we conduct a low-beta resistive magnetohydrodynamics simulation of this observed event. We drive the coronal evolution by line-tied diverging boundary motions, so as to emulate the observed photospheric flow pattern associated with some magnetic flux emergence. The numerical analysis allows us to explain several observed features of the confined flare. The vorticity induced in the fan by the prescribed motions causes the spines to tear apart along the fan. This leads to formation of a thin current sheet and induces null-point reconnection. We also find that the null point and its associated topological structure is embedded within QSLs, already present in the asymmetric potential field configuration. We find that the QSL footprints correspond to the observed elongated spine ribbons. Finally, we observe that before and after reconnecting at the null point, all field lines undergo slipping and slip-running reconnection within the QSLs. Field lines, and therefore particle impacts, slip or slip-run according to their distance from the spine, in directions and over distances that are compatible with the observed dynamics of the ribbons.
To study the buildup of a magnetic flux rope before a major flare and coronal mass ejection (CME), we compute the magnetic helicity injection, twist accumulation, and topology structure of the ...three-dimensional (3D) magnetic field, which is derived by the nonlinear force-free field model. The Extreme-ultraviolet Imaging Telescope on board the Solar and Heliospheric Observatory observed a series of confined flares without any CME before a major flare with a CME at 23:02 UT on 2005 January 15 in active region NOAA 10720. We derive the vector velocity at eight time points from 18:27 UT to 22:20 UT with the differential affine velocity estimator for vector magnetic fields, which were observed by the Digital Vector Magnetograph at Big Bear Solar Observatory. The injected magnetic helicity is computed with the vector magnetic and velocity fields. The helicity injection rate was (-16.47+ or -3.52) x 10 super(40) Mx super(2) hr super(-1). We find that only about 1.8% of the injected magnetic helicity became the internal helicity of the magnetic flux rope, whose twist increasing rate was -0.18 + or - 0.08 Turns hr super(-1). The quasi-separatrix layers (QSLs) of the 3D magnetic field are computed by evaluating the squashing degree, Q. We find that the flux rope was wrapped by QSLs with large Q values, where the magnetic reconnection induced by the continuously injected magnetic helicity further produced the confined flares. We suggest that the flux rope was built up and heated by the magnetic reconnection in the QSLs.
Context. The standard model for eruptive flares has been extended to three dimensions (3D) in the past few years. This model predicts typical J-shaped photospheric footprints of the coronal current ...layer, forming at similar locations as the quasi-separatrix layers (QSLs). Such a morphology is also found for flare ribbons observed in the extreme ultraviolet (EUV) band, and in nonlinear force-free field (NLFFF) magnetic field extrapolations and models. Aims. We study the evolution of the photospheric traces of the current density and flare ribbons, both obtained with the Solar Dynamics Observatory instruments. We aim to compare their morphology and their time evolution, before and during the flare, with the topological features found in a NLFFF model. Methods. We investigated the photospheric current evolution during the 06 September 2011 X-class flare (SOL2011-09-06T22:20) occurring in NOAA AR 11283 from observational data of the magnetic field obtained with the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory. We compared this evolution with that of the flare ribbons observed in the EUV filters of the Atmospheric Imager Assembly. We also compared the observed electric current density and the flare ribbon morphology with that of the QSLs computed from the flux rope insertion method-NLFFF model. Results. The NLFFF model shows the presence of a fan-spine configuration of overlying field lines, due to the presence of a parasitic polarity, embedding an elongated flux rope that appears in the observations as two parts of a filament. The QSL signatures of the fan configuration appear as a circular flare ribbon that encircles the J-shaped ribbons related to the filament ejection. The QSLs, evolved via a magnetofrictional method, also show similar morphology and evolution as both the current ribbons and the EUV flare ribbons obtained several times during the flare. Conclusions. For the first time, we propose a combined analysis of the photospheric traces of an eruptive flare, in a complex topology, with direct measurements of electric currents and QSLs from observational data and a magnetic field model. The results, obtained by two different and independent approaches 1) confirm previous results of current increase during the impulsive phase of the flare and 2) show how NLFFF models can capture the essential physical signatures of flares even in a complex magnetic field topology.
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