E. Pariat

The 2011 February 15 X2 Flare, Ribbons, Coronal Front, and Mass Ejection: Interpreting the Three-dimensional Views from the Solar Dynamics Observatory and STEREO Guided by Magnetohydrodynamic Flux-rope Modeling

The 2011 February 15 X2.2 flare and associated Earth-directed halo coronal mass ejection were observed in unprecedented detail with high resolution in spatial, temporal, and thermal dimensions by the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory, as well as by instruments on the two STEREO spacecraft, then at near-quadrature relative to the Sun-Earth line. These observations enable us to see expanding loops from a flux-rope-like structure over the shearing polarity-inversion line between the central δ-spot groups of AR 11158, developing a propagating coronal front (EIT wave), and eventually forming the coronal mass ejection moving into the inner heliosphere. The observations support the interpretation that all of these features, including the EIT wave, are signatures of an expanding volume traced by loops (much larger than the flux rope only), surrounded by a moving front rather than predominantly wave-like perturbations; this interpretation is supported by previously published MHD models for active-region and global scales. The lateral expansion of the eruption is limited to the local helmet-streamer structure and halts at the edges of a large-scale domain of connectivity (in the process exciting loop oscillations at the edge of the southern polar coronal hole). The AIA observations reveal that plasma warming occurs within the expansion front as it propagates over quiet Sun areas. This warming causes dimming in the 171 A (Fe IX and Fe X) channel and brightening in the 193 and 211 A (Fe XII-XIV) channels along the entire front, while there is weak 131 A (Fe VIII and Fe XXI) emission in some directions. An analysis of the AIA response functions shows that sections of the front running over the quiet Sun are consistent with adiabatic warming; other sections may require additional heating which MHD modeling suggests could be caused by Joule dissipation. Although for the events studied here the effects of volumetric expansion are much more obvious than true wave phenomena, we discuss how different magnetic environments within and around the erupting region can lead to the signatures of either or both of these aspects.

Current sheet formation in quasi-separatrix layers and hyperbolic flux tubes

In 3D magnetic field configurations, quasi-separatrix layers (QSLs) are defined as volumes in which field lines locally display strong gradients of connectivity. Considering QSLs both as the preferential locations for current sheet development and magnetic reconnection, in general, and as a natural model for solar flares and coronal heating, in particular, has been strongly debated issues over the past decade. In this paper, we perform zero-β resistive MHD simulations of the development of electric currents in smooth magnetic configurations which are, strictly speaking, bipolar though they are formed by four flux concentrations, and whose potential fields contain QSLs. The configurations are driven by smooth and large-scale sub-Alfvenic footpoint motions. Extended electric currents form naturally in the configurations, which evolve through a sequence of quasi non-linear force-free equilibria. Narrow current layers also develop. They spontaneously form at small scales all around the QSLs, whatever the footpoint motions are. For long enough motions, the strongest currents develop where the QSLs are the thinnest, namely at the Hyperbolic Flux Tube (HFT), which generalizes the concept of separator. These currents progressively take the shape of an elongated sheet, whose formation is associated with a gradual steepening of the magnetic field gradients over tens of Alfven times, due to the different motions applied to the field lines which pass on each side of the HFT. Our model then self-consistently accounts for the long-duration energy storage prior to a flare, followed by a switch-on of reconnection when the currents reach the dissipative scale at the HFT. In configurations whose potential fields contain broader QSLs, when the magnetic field gradients reach the dissipative scale, the currents at the HFT reach higher magnitudes. This implies that major solar flares which are not related to an early large-scale ideal instability, must occur in regions whose corresponding potential fields have broader QSLs. Our results lead us to conjecture that physically, current layers must always form on the scale of the QSLs. This implies that electric currents around QSLs may be gradually amplified in time only if the QSLs are broader than the dissipative length-scale. We also discuss the potential role of QSLs in coronal heating in bipolar configurations made of a continuous distribution of flux concentrations.

Three-Dimensional Modeling of Quasi-Homologous Solar Jets

Recent solar observations (e.g., obtained with Hinode and STEREO) have revealed that coronal jets are a more frequent phenomenon than previously believed. This higher frequency results, in part, from the fact that jets exhibit a homologous behavior: successive jets recur at the same location with similar morphological features. We present the results of three-dimensional (3D) numerical simulations of our model for coronal jets. This study demonstrates the ability of the model to generate recurrent 3D untwisting quasi-homologous jets when a stress is constantly applied at the photospheric boundary. The homology results from the property of the 3D null-point system to relax to a state topologically similar to its initial configuration. In addition, we find two distinct regimes of reconnection in the simulations: an impulsive 3D mode involving a helical rotating current sheet that generates the jet and a quasi-steady mode that occurs in a 2D-like current sheet located along the fan between the sheared spines. We argue that these different regimes can explain the observed link between jets and plumes.

Sigmoidal Active Region on the Sun: Comparison of a Magnetohydrodynamical Simulation and a Nonlinear Force-free Field Model

In this paper we show that when accurate nonlinear force-free field (NLFFF) models are analyzed together with high-resolution magnetohydrodynamic (MHD) simulations, we can determine the physical causes for the coronal mass ejection (CME) eruption on 2007 February 12. We compare the geometrical and topological properties of the three-dimensional magnetic fields given by both methods in their pre-eruptive phases. We arrive at a consistent picture for the evolution and eruption of the sigmoid. Both the MHD simulation and the observed magnetic field evolution show that flux cancellation plays an important role in building the flux rope. We compute the squashing factor, Q, in different horizontal maps in the domains. The main shape of the quasi-separatrix layers (QSLs) is very similar between the NLFFF and MHD models. The main QSLs lie on the edge of the flux rope. While the QSLs in the NLFFF model are more complex due to the intrinsic large complexity in the field, the QSLs in the MHD model are smooth and possess lower maximum value of Q. In addition, we demonstrate the existence of hyperbolic flux tubes (HFTs) in both models in vertical cross sections of Q. The main HFT, located under the twisted flux rope in both models, is identified as the most probable site for reconnection. We also show that there are electric current concentrations coinciding with the main QSLs. Finally, we perform torus instability analysis and show that a combination between reconnection at the HFT and the resulting expansion of the flux rope into the torus instability domain is the cause of the CME in both models.

Estimation of the squashing degree within a three-dimensional domain

Context. The study of the magnetic topology of magnetic elds 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 eld-line invariant quantifying the deformation of elementary ux tubes. QSL are complex and thin three-dimensional (3D) structures dicult 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 signicantly dierent. 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 congurations: a theoretical case and a non-linear force free conguration derived from observations. Conclusions. The representation of QSL through 2D planar cuts is an ecient procedure to derive the geometry of these structures and to relate them with other quantities, e.g. electric currents and plasma ows. It will enforce a more direct comparison of the role of QSL in magnetic reconnection.

TWIST ACCUMULATION AND TOPOLOGY STRUCTURE OF A SOLAR MAGNETIC FLUX ROPE

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 ± 3.52) × 1040 Mx2 hr–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 ± 0.08 Turns hr–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.

Model for straight and helical solar jets - I. Parametric studies of the magnetic field geometry

Context. Jets are dynamic, impulsive, well-collimated plasma events developing at many di erent scales and in di erent layers of the solar atmosphere. Aims. Jets are believed to be induced by magnetic reconnection, a process central to many astrophysical phenomena. Studying their dynamics can help us to better understand the processes acting in larger eruptive events (e.g., ares and coronal mass ejections) as well as mass, magnetic helicity, and energy transfer at all scales in the solar atmosphere. The relative simplicity of their magnetic geometry and topology, compared with larger solar active events, makes jets ideal candidates for studying the fundamental role of reconnection in energetic events. Methods. In this study, using our recently developed numerical solver ARMS, we present several parametric studies of a 3D numerical magneto-hydrodynamic model of solar-jet-like events. We studied the impact of the magnetic eld inclination and photospheric eld distribution on the generation and properties of two morphologically di erent types of solar jets, straight and helical, which can account for the observed so-called standard and blowout jets. Results.Our parametric studies validate our model of jets for di erent geometric properties of the magnetic con guration. We nd that a helical jet is always triggered for the range of parameters we tested. This demonstrates that the 3D magnetic null-point con guration is a very robust structure for the energy storage and impulsive release characteristic of helical jets. In certain regimes determined by magnetic geometry, a straight jet precedes the onset of a helical jet. We show that the reconnection occurring during the straight-jet phase in uences the triggering of the helical jet. Conclusions. Our results allow us to better understand the energization, triggering, and driving processes of straight and helical jets. Our model predicts the impulsiveness and energetics of jets in terms of the surrounding magnetic eld con guration. Finally, we discuss the interpretation of the observationally de ned standard and blowout jets in the context of our model, as well as the physical factors that determine which type of jet will occur.

X-ray and ultraviolet investigation into the magnetic connectivity of a solar flare

We investigate the X-ray and UV emission detected by RHESSI and TRACE in the context of a solar flare on the 16th November 2002 with the goal of better understanding the evolution of the flare. We analysed the characteristics of the X-ray emission in the 12–25 and 25–50 keV energy range while we looked at the UV emission at 1600 A . The flare appears to have two distinct phases of emission separated by a 25-s time delay, with the first phase being energetically more important. We found good temporal and spatial agreement between the 25–50 keV X-rays and the most intense areas of the 1600 A UV emission. We also observed an extended 100-arcsec < 25 keV source that appears coronal in nature and connects two separated UV ribbons later in the flare. Using the observational properties in X-ray and UV wavelengths, we propose two explanations for the flare evolution in relation to the spine/fan magnetic field topology and the accelerated electrons. We find that a combination of quasi separatrix layer reconnection and null-point reconnection is required to account for the observed properties of the X-ray and UV emission.

Interchange Slip-Running Reconnection and Sweeping SEP Beams

We present a new model to explain how particles (solar energetic particles; SEPs), accelerated at a reconnection site that is not magnetically connected to the Earth, could eventually propagate along the well-connected open flux tube. Our model is based on the results of a low-β resistive magnetohydrodynamics simulation of a three-dimensional line-tied and initially current-free bipole, which is embedded in a non-uniform open potential field. The topology of this configuration is that of an asymmetric coronal null point, with a closed fan surface and an open outer spine. When driven by slow photospheric shearing motions, field lines, initially fully anchored below the fan dome, reconnect at the null point, and jump to the open magnetic domain. This is the standard interchange mode as sketched and calculated in 2D. The key result in 3D is that reconnected open field lines located in the vicinity of the outer spine keep reconnecting continuously, across an open quasi-separatrix layer, as previously identified for non-open-null-point reconnection. The apparent slipping motion of these field lines leads to formation of an extended narrow magnetic flux tube at high altitude. Because of the slip-running reconnection, we conjecture that if energetic particles would be traveling through, or be accelerated inside, the diffusion region, they would be successively injected along continuously reconnecting field lines that are connected farther and farther from the spine. At the scale of the full Sun, owing to the super-radial expansion of field lines below 3xa0R⊙, such energetic particles could easily be injected in field lines slipping over significant distances, and could eventually reach the distant flux tube that is well-connected to the Earth.

Filament Interaction Modeled by Flux Rope Reconnection

Hα observations of solar active region NOAA 10501 on 2003 November 20 revealed a very uncommon dynamic process: during the development of a nearby flare, two adjacent elongated filaments approached each other, merged at their middle sections, and separated again, thereby forming stable configurations with new footpoint connections. The observed dynamic pattern is indicative of slingshot reconnection between two magnetic flux ropes. We test this scenario by means of a three-dimensional zero β magnetohydrodynamic simulation, using a modified version of the coronal flux rope model by Titov and Demoulin as the initial condition for the magnetic field. To this end, a configuration is constructed that contains two flux ropes which are oriented side-by-side and are embedded in an ambient potential field. The choice of the magnetic orientation of the flux ropes and of the topology of the potential field is guided by the observations. Quasi-static boundary flows are then imposed to bring the middle sections of the flux ropes into contact. After sufficient driving, the ropes reconnect and two new flux ropes are formed, which now connect the former adjacent flux rope footpoints of opposite polarity. The corresponding evolution of filament material is modeled by calculating the positions of field line dips at all times. The dips follow the morphological evolution of the flux ropes, in qualitative agreement with the observed filaments.