G. Aulanier

What is the source of the magnetic helicity shed by CMEs? The long-term helicity budget of AR 7978

An isolated active region (AR) was observed on the Sun during seven rotations, starting from its birth in July 1996 to its full dispersion in December 1996. We analyse the long-term budget of the AR relative magnetic helicity. Firstly, we calculate the helicity injected by differential rotation at the photospheric level using MDI/SoHO magnetograms. Secondly, we compute the coronal magnetic field and its helicity selecting the model which best fits the soft X-ray loops observed with SXT/Yohkoh. Finally, we identify all the coronal mass ejections (CMEs) that originated from the AR during its lifetime using LASCO and EIT/SoHO. Assuming a one to one correspondence between CMEs and magnetic clouds, we estimate the magnetic helicity which could be shed via CMEs. We find that differential rotation can neither provide the required magnetic helicity to the coronal field (at least a factor 2.5 to 4 larger), nor to the field ejected to the interplanetary space (a factor 4 to 20 larger), even in the case of this AR for which the total helicity injected by differential rotation is close to the maximum possible value. However, the total helicity ejected is equivalent to that of a twisted flux tube having the same magnetic flux as the studied AR and a number of turns in the interval [0.5, 2.0]. We suggest that the main source of helicity is the inherent twist of the magnetic flux tube forming the active region. This magnetic helicity is transferred to the corona either by the continuous emergence of the flux tube for several solar rotations (i.e. on a time scale much longer than the classical emergence phase), or by torsional Alfven waves.

RESISTIVE EMERGENCE OF UNDULATORY FLUX TUBES

During its 2000 January flight, the Flare Genesis Experiment observed the gradual emergence of a bipolar active region, by recording a series of high-resolution photospheric vector magnetograms and images in the blue wing of the Hα line. Previous analyses of these data revealed the occurrence of many small-scale, transient Hα brightenings identified as Ellerman bombs (EBs). They occur during the flux emergence, and many of them are located near moving magnetic dipoles in which the vector magnetic field is nearly tangential to the photosphere. A linear force-free field extrapolation of one of the magnetograms was performed to study the magnetic topology of small-scale EBs and their possible role in the flux emergence process. We found that 23 out of 47 EBs are cospatial with bald patches (BPs), while 15 are located at the footpoints of very flat separatrix field lines passing through distant BPs. We conclude that EBs can be due to magnetic reconnection, not only at BP locations, but also along their separatrices, occurring in the low chromosphere. The topological analysis reveals, for the first time, that many EBs and BPs are linked by a hierarchy of elongated flux tubes showing aperiodic spatial undulations, whose wavelengths are typically above the threshold of the Parker instability. These findings suggest that arch filament systems and coronal loops do not result from the smooth emergence of large-scale Ω-loops from below the photosphere, but rather from the rise of undulatory flux tubes whose upper parts emerge because of the Parker instability and whose dipped lower parts emerge because of magnetic reconnection. EBs are then the signature of this resistive emergence of undulatory flux tubes.

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.

CRITERIA FOR FLUX ROPE ERUPTION: NON-EQUILIBRIUM VERSUS TORUS INSTABILITY

The coronal magnetic configuration of an active region typically evolves quietly for a few days before becoming suddenly eruptive and launching a coronal mass ejection (CME). The precise origin of the eruption is still under debate. The loss of equilibrium, or an ideal magnetohydrodynamic (MHD) instability such as torus instability are among the several mechanisms that have proposed to be responsible for the sudden eruptions. Distinct approaches have also been formulated for limited cases having circular or translation symmetry. We revisit the previous theoretical approaches setting them in the same analytical framework. The coronal field results from the contribution of a non-neutralized current channel added to a background magnetic field, which in our model is the potential field generated by two photospheric flux concentrations. The evolution on short Alfvenic timescale is governed by ideal MHD. We first show analytically that the loss of equilibrium and the stability analysis are two different views of the same physical mechanism. Second, we identify that the same physics is involved in the instabilities of circular and straight current channels. Indeed, they are just two particular limiting cases of more general current paths. A global instability of the magnetic configuration is present when the current channel is located at a coronal height, h, large enough so that the decay index of the potential field, ∂ln |B p|/∂ln h, is larger than a critical value. At the limit of very thin current channels, previous analysis has found critical decay indices of 1.5 and 1 for circular and straight current channels, respectively. However, with current channels being deformable and as thick as that expected in the corona, we show that this critical index has similar values for circular and straight current channels, and is typically in the range [1.1,1.3].

The standard flare model in three dimensions - I. Strong-to-weak shear transition in post-flare loops

Context. The standard CSHKP model for eruptive flares is two-dimensional. Yet observational interpretations of photospheric currents in pre-eruptive sigmoids, shear in post-flare loops, and relative positioning and shapes of flare ribbons, all together require threedimensional extensions to the model. Aims. We focus on the strong-to-weak shear transition in post-flare loops, and on the time-evolution of the geometry of photospheric electric currents, which occur during the development of eruptive flares. The objective is to understand the three-dimensional physical processes, which cause them, and to know how much the post-flare and the pre-eruptive distributions of shear depend on each other. Methods. The strong-to-weak shear transition in post-flare loops is identified and quantified in a flare observed by STEREO, as well as in a magnetohydrodynamic simulation of CME initiation performed with the OHM code. In both approaches, the magnetic shear is evaluated with field line footpoints. In the simulation, the shear is also estimated from ratios between magnetic field components. Results. The modeled strong-to-weak shear transition in post-flare loops comes from two effects. Firstly, a reconnection-driven transfer of the differential magnetic shear, from the preto the post-eruptive configuration. Secondly, a vertical straightening of the inner legs of the CME, which induces an outer shear weakening. The model also predicts the occurrence of narrow electric current layers inside J-shaped flare ribbons, which are dominated by direct currents. Finally, the simulation naturally accounts for energetics and time-scales for weak and strong flares, when typical scalings for young and decaying solar active regions are applied. Conclusions. The results provide three-dimensional extensions to the standard flare model. These extensions involve MHD processes that should be tested with observations.

SOLAR PROMINENCE INTERACTIONS

We report numerical simulations of the formation, interaction, and magnetic reconnection between pairs of solar prominences within the sheared-arcade model. Our experiments consider the four possible basic combinations of chiralities (identical or opposite) and axial magnetic fields (aligned or opposed) between the participating prominences. When the topology of the global flux system comprising the prominences and arcades is bipolar, so that a single polarity inversion line is shared by the two structures, then identical chiralities necessarily imply aligned axial fields, while opposite chiralities imply opposed axial fields. In the former case, external magnetic reconnections forming field lines linking the two prominences occur; in the latter, such reconnections are disfavored, and no linkage takes place. These results concur with empirical rules for prominence interactions. When the topology instead is quadrupolar, so that a second polarity inversion line crossing the first lies between the prominences, then the converse relation holds between chirality and axial-field alignment. External reconnections forming linking field lines now occur between prominences with opposite chiralities; they also occur, but result only in footpoint exchanges, between prominences with identical chiralities. These findings conflict with the accepted empirical rules but may not have been tested in observations to date. All of our model prominences, especially those that undergo linking reconnections, contain substantial magnetic shear and twist. Nevertheless, none exhibits any sign of onset of instability or loss of equilibrium that might culminate in an eruption.

Equilibrium and observational properties of line-tied twisted flux tubes

We describe a new explicit three-dimensional magnetohydrodymanic code, which solves the standard zero-β MHD equations in Cartesian geometry, with line-tied conditions at the lower boundary and open conditions at the other ones. Using this code in the frame of solar active regions, we simulate the evolution of an initially potential and concentrated bipolar magnetic field, subject to various sub-Alfvenic photospheric twisting motions which preserve the initial photospheric vertical magnetic field. Both continuously driven and relaxation runs are performed. Within the numerical domain, a steep equilibrium curve is found for the altitude of the apex of the field line rooted in the vortex centers as a function of the twist. Its steepness strongly depends on the degree of twist in outer field lines rooted in weak field regions. This curve fits the analytical expression for the asymptotic behaviour of force-free fields of spherical axisymmetric dipoles subject to azimuthal shearing motions, as well as the curve derived for other line-tied twisted flux tubes reported in previous works. This suggests that it is a generic prop- erty of line-tied sheared/twisted arcades. However, contrary to other studies we never find a transition toward a non-equilibrium within the numerical domain, even for twists corresponding to steep regions of the equilibrium curve. The calculated configura- tions are analyzed in the frame of solar observations. We discuss which specific conditions are required for the steepness of the generic equilibrium curve to result in dynamics which are typical of both fast and slow CMEs observed below 3 R� .W e pro- vide natural interpretations for the existence of asymmetric and multiple concentrations of electric currents in homogeneoulsy twisted sunspots, due to the twisting of both short and long field lines. X-ray sigmoids are reproduced by integrating the Joule heating term along the line-of-sight. These sigmoids have inverse-S shapes associated with negative force-free parameters α, which is consistent with observed rules in the northern solar hemisphere. We show that our sigmoids are not formed in the main twisted flux tube, but rather in an ensemble of low-lying sheared and weakly twisted field lines, which individually never trace the whole sigmoid, and which barely show their distorded shapes when viewed in projection. We find that, for a given bipolar configuration and a given twist, neither the α nor the altitude of the lines whose envelope is a sigmoid depends on the vortex size.

Differential Magnetic Field Shear in an Active Region

The three-dimensional extrapolation of magnetic field lines from a magnetogram obtained at Kitt Peak allows us to understand the global structure of the NOAA active region 6718, as observed in X-rays with the Normal Incidence X-ray Telescope (NIXT) and in Ha with the Multichannel Subtractive Double Pass spectrograph (MSDP) in Meudon on 1991 July 11. This active region was in a quiet stage. Bright X-ray loops connect plages having field strengths of approx. 300 G, while H-alpha fibriles connect penumbrae having strong spot fields to the surrounding network. Small, intense X-ray features in the moat region around a large spot, which could be called X-ray-bright points, are due mainly to the emergence of magnetic flux and merging of these fields with surrounding ones. A set of large-scale, sheared X-ray loops is observed in the central part of the active region. Based on the fit between the observed coronal structure and the field configurations (and assuming a linear force-free field), we propose a differential magnetic field shear model for this active region. The decreasing shear in outer portions of the active region may indicate a continual relaxation of the magnetic field to a lower energy state in the progressively older portions of the AR.

The standard flare model in three dimensions - III. Slip-running reconnection properties

Context. A standard model for eruptive flares aims at describing observational 3D features of the reconnecting coronal magnetic field. Extensions to the 2D model require the physical understanding of 3D reconnection processes at the origin of the magnetic configuration evolution. However, the properties of 3D reconnection without null point and separatrices still need to be analyzed. Aims. 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. Methods. We studied the slip-running reconnection of field lines in a magnetohydrodynamic simulation of an eruptive flare associated with a torus-unstable flux rope. The squashing degree and the mapping norm are two parameters related to the QSLs. We computed them to investigate their relation with the slip-running reconnection speed of selected field lines. Results. Field lines associated with the flux rope and the flare loops undergo a continuous series of magnetic reconnection, which results in their super-Alfvenic slipping motion. The time profile of their slippage speed and the space distribution of the mapping norm are shown to be strongly correlated. We find that the motion speed is proportional to the mapping norm. Moreover, this slip-running motion becomes faster as the flux rope expands, since the 3D current layer evolves toward a current sheet, and QSLs to separatrices. Conclusions. 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.

ELECTRIC CURRENTS IN FLARE RIBBONS: OBSERVATIONS AND THREE-DIMENSIONAL STANDARD MODEL

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 flares 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.