Jean-Jacques Aly

Characterizing and predicting the magnetic environment leading to solar eruptions

The physical mechanism responsible for coronal mass ejections has been uncertain for many years, in large part because of the difficulty of knowing the three-dimensional magnetic field in the low corona. Two possible models have emerged. In the first, a twisted flux rope moves out of equilibrium or becomes unstable, and the subsequent reconnection then powers the ejection. In the second, a new flux rope forms as a result of the reconnection of the magnetic lines of an arcade (a group of arches of field lines) during the eruption itself. Observational support for both mechanisms has been claimed. Here we report modelling which demonstrates that twisted flux ropes lead to the ejection, in support of the first model. After seeing a coronal mass ejection, we use the observed photospheric magnetic field in that region from four days earlier as a boundary condition to determine the magnetic field configuration. The field evolves slowly before the eruption, such that it can be treated effectively as a static solution. We find that on the fourth day a flux rope forms and grows (increasing its free energy). This solution then becomes the initial condition as we let the model evolve dynamically under conditions driven by photospheric changes (such as flux cancellation). When the magnetic energy stored in the configuration is too high, no equilibrium is possible and the flux rope is ‘squeezed’ upwards. The subsequent reconnection drives a mass ejection.

Coronal Mass Ejection Initiation: On the Nature of the Flux Cancellation Model

We consider a three-dimensional bipolar force-free magnetic field with a nonzero magnetic helicity, occupying a half-space, and study the problem of its evolution driven by an imposed photospheric flux decrease. For this specific setting of the Flux Cancellation Model describing coronal mass ejections occurring in active regions, we address the issues of the physical meaning of flux decrease, of the influence on field evolution of the size of the domain over which this decrease is imposed, and of the existence of an energetic criterion characterizing the possible onset of disruption of the configuration. We show that (1) the imposed flux disappearance can be interpreted in terms of transport of positive and negative fluxes toward the inversion line, where they get annihilated. (2) For the particular case actually computed, in which the initial state is quite sheared, the formation of a twisted flux rope and the subsequent global disruption of the configuration are obtained when the flux has decreased by only a modest amount over a limited part of the whole active region. (3) The disruption is produced when the magnetic energy becomes of the order of the decreasing energy of a semi-open field, and then before reaching the energy of the associated fully open field. This suggests that the mechanism leading to the disruption is nonequilibrium as in the case where flux is imposed to decrease over the whole region.

CORONAL MASS EJECTION INITIATION BY CONVERGING PHOTOSPHERIC FLOWS: TOWARD A REALISTIC MODEL

In the context of coronal mass ejections triggering, we reconsider the class of models in which the evolution of an active region (AR) is driven by imposed boundary motions converging toward the polarity inversion line (PIL). We introduce a new model problem in which there is a large-scale flow with a diverging structure on the photosphere. This flow is reminiscent of that of the well-known moat flow around each of the two spots of a bipolar AR and transports only part of the magnetic flux toward the PIL. It is thus more compatible with observations than the one used in our previous study, which forced the whole positive and negative polarity parts of the AR approaching each other. We also include a diffusion term associated with small-scale turbulent photospheric motions, but keep the associated diffusivity at a low value in the particular study described here. We show that the evolution of an initial sheared force-free field first leads to the formation of a twisted flux rope which stays in equilibrium for some time. Eventually, however, the configuration suffers a global disruption whose underlying mechanism is found by energetic considerations to be nonequilibrium. It begins indeed when the magnetic energy becomes of the order of the energy of an accessible partially open field. For triggering an eruption by converging flows, it is thus not necessary to advect the whole AR toward the PIL, but only its central part.

Reconstruction of the solar coronal magnetic field in spherical geometry

Context. High-resolution vector magnetographs either onboard spacecrafts or satellites (HMI/SDO, etc.) or ground based (SOLIS, etc.) now gives access to vector synoptic maps, composite magnetograms made of multiple interactive active regions, and full disk magnetograms. It thus become possible to reconstruct the coronal magnetic field on the full Sun scale. Aims. We present a method for reconstructing the global solar coronal magnetic field as a nonlinear force-free field. It is based on a well-posed Grad-Rubin iterative scheme adapted to spherical coordinates Methods. This method is a natural extension to spherical geometry of the one we previously developed in Cartesian geometry. It is implemented in the code XTRAPOLS, which is a massively parallel code. It allows dealing with the strong constraints put on the computational methods by having to handle the very large amounts of data contained in high-resolution large-scale magnetograms. The method exploits the mixed elliptic-hyperbolic nature of the Grad-Rubin boundary value problem. It uses a finite-di erence method for the elliptic part and a method of characteristics for the hyperbolic part. The computed field guarantees to be divergence free up to round-o errors, by introducing a representation in terms of a vector potential satisfying specific gauge conditions. The construction of the latter ‐ called here the restricted DeVore gauge ‐ is described in detail in an appendix. Results. We show that XTRAPOLS performs well by applying it to the reconstruction of a particular semi-analytic force-free field that has already been considered by various authors.

Non-current-free coronal closure of subphotospheric MHD models

We propose a method that allows the matching of two classes of models that have been well developed so far, but largely independently from each other: (1) convection zone (CZ) models, which generally either end up below the photosphere or are matched with an external potential field, and (2) coronal models of eruptive processes and heating, which usually consider the evolution of current-carrying magnetic fields driven by given photospheric changes. In our approach, the thin turbulent photospheric layer between the two large regions is modeled as a resistive layer across which the physical quantities suffer stiff variations. We show that this layer enables the transport of an electric current into the corona through the tangential component of the electric field (continuous across the various interfaces), as well as good conservation of the global magnetic helicity. To illustrate our general approach, we present in detail a model problem in which the rising of an initially twisted flux rope through the CZ is described kinematically while the physics inside the corona is described by a full magnetohydrodynamic model. We show that the evolution leads to the emergence of magnetic flux and electric current into the corona, with the creation of a flux rope that eventually suffers a dynamical transition toward fast expansion.

DOES THE COMPRESSION OR THE EXPANSION OF A SIMPLE TOPOLOGY POTENTIAL MAGNETIC FIELD LEAD TO THE DEVELOPMENT OF CURRENT SHEETS

Janse & Low have most recently addressed the following question. Consider a cylindrical domain containing a simple topology potential magnetic field threading its lower and upper horizontal faces, and a perfectly conducting plasma. Suppose that this domain is made to slowly contract or expand in the vertical direction, so driving the field into a quasi-static evolution through a series of force-free configurations. Then are these configurations smooth, or do they contain current sheets (CSs)? We reexamine here their three-step argument leading to the conclusion that CSs form most generally. We prove analytically that the field has to evolve through “topologically untwisted” and “nonpotential” configurations, thus confirming the first two steps. However, we find the third step—leading to the conclusion that a smooth untwisted force-free field is necessarily potential—to be very disputable.

Small-scale dynamo magnetism as the driver for heating the solar atmosphere

The long-standing problem of how the solar atmosphere is heated has been addressed by many theoretical studies, which have stressed the relevance of two specific mechanisms, involving magnetic reconnection and waves, as well as the necessity of treating the chromosphere and corona together. But a fully consistent model has not yet been constructed and debate continues, in particular about the possibility of coronal plasma being heated by energetic phenomena observed in the chromosphere. Here we report modelling of the heating of the quiet Sun, in which magnetic fields are generated by a subphotospheric fluid dynamo intrinsically connected to granulation. We find that the fields expand into the chromosphere, where plasma is heated at the rate required to match observations (4,500 watts per square metre) by small-scale eruptions that release magnetic energy and drive sonic motions. Some energetic eruptions can even reach heights of 10 million metres above the surface of the Sun, thereby affecting the very low corona. Extending the model by also taking into account the vertical weak network magnetic field allows for the existence of a mechanism able to heat the corona above, while leaving unchanged the physics of chromospheric eruptions. Such a mechanism rests on the eventual dissipation of Alfvén waves generated inside the chromosphere and that carry upwards the required energy flux of 300 watts per square metre. The model shows a topologically complex magnetic field of 160 gauss on the Sun’s surface, agreeing with inferences obtained from spectropolarimetric observations, chromospheric features (contributing only weakly to the coronal heating) that can be identified with observed spicules and blinkers, and vortices that may be possibly associated with observed solar tornadoes.

Nonlinear Stability of a Class of Magnetostatic Equilibria with an Application to Solar Prominences

We consider a particular class of three-dimensional magnetostatic equilibria in which the plasma is submitted to a vertical gravitational field and the gradient of the total (thermal+magnetic) pressure vanishes. We show analytically that an equilibrium in that class makes the energy an absolute minimum in the set of all the configurations accessible from it by an arbitrary finite deformation constrained by ideal MHD and imposed to vanish on a rigid conducting wall (line-tying condition). Along with energy conservation, this implies the nonlinear ideal stability of that equilibrium in the following sense. Suppose that a perturbation of energy w(0) is applied at time t = 0 and thus evolves by obeying the nonlinear MHD equations. Then some measure of the sizes of the plasma velocity and the deformation of the structure can be made to stay at any t ≥ 0 below an arbitrarily prescribed value by choosing w(0) small enough. Nonlinear stability also holds true for a configuration obtained by superposing an equilibrium of the previous type and a nonmagnetic equilibrium which is also an energy minimizer—for instance an equilibrium with uniform specific entropy, which is shown to have that property. Our result applies to a subset of a family of equilibria, computed by B. C. Low, which includes in particular the standard Kippenhahn-Schluter model describing the magnetic support of solar corona prominences.

CORONAL CLOSURE OF SUBPHOTOSPHERIC MHD CONVECTION FOR THE QUIET SUN

We use our resistive layer model (RLM), which stresses the importance of the resistivity at the photospheric interface, to study the evolution of a solar coronal quiet region driven by subphotospheric convection. The initial version of the RLM is improved by introducing a new Boussinesq MHD model for the upper part of the convection zone (CZ), while the low-beta corona is still described by a MHD model. We compute the evolution of a weak magnetic field introduced initially in the CZ. We observe its amplification by the turbulence, the concentration of the photospheric flux at the boundaries of the convection cells, the coalescence and the cancellation of flux elements, and the transfer of about 10% of the magnetic energy into the corona. The currents associated with the nonpotential coronal field are found to be organized in filament-like localized structures due to the photospheric vortices and the complexity of the magnetic topology. Their resistive dissipation contributes to the heating of the quiet corona.

Magnetic flux ropes: Fundamental structures for eruptive phenomena

We consider some general aspects of twisted magnetic flux ropes (TFR), which are thought to play a fundamental role in the structure and dynamics of large scale eruptive events. We first discuss the possibility to show the presence of a TFR in a pre-eruptive configuration by using a model along with observational informations provided by a vector magnetograph. Then we present, in the framework of a generic model in which the coronal field is driven into an evolution by changes imposed at the photospheric level, several mechanisms which may lead to the formation and the disruption of a TFR, including the development of a MHD instability, and we discuss the issues of the energy and helicity contents of an erupting configuration. Finally we report some results of a recent and more ambitious approach to the physics of TFRs in which one tries to describe in a consistent way their rising through the convection zone, their emergence through the photosphere, and their subsequent evolution in the corona.