K. Galsgaard

3D simulations identifying the effects of varying the twist and field strength of an emerging flux tube

Aims. We investigate the effects of varying the magnetic field strength and the twist of a flux tube as it rises through the solar interior and emerges into the atmosphere. Methods. Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer. The specific balance of forces chosen results in the tube being fully buoyant and the temperature is decreased in the ends of the tube to encourage the formation of an Ω-shape along the tube’s length. We vary the magnetic field strength and twist independently of each other so as to give clear results of the individual effects of each parameter. Results. We find a self-similar evolution in the rise and emergence of the flux tube when the magnetic field strength of the tube is modified. During the rise through the solar interior, the height of the crest and axis, the velocity of the crest and axis, and the decrease in the magnetic field strength of the axis of the tube are directly dependent upon the initial magnetic field strength given to the tube. No such self-similarity is evident when the twist of the flux tube is changed, due to the complex interaction of the tension force on the rise of the tube. For low magnetic field strength and twist values, we find that the tube cannot fully emerge into the atmosphere once it reaches the top of the interior since the buoyancy instability criterion cannot be fulfilled. For those tubes that do advance into the atmosphere, when the magnetic field strength has been modified, we find further self-similar behaviour in the amount of tube flux transported into the atmosphere. For the tubes that do emerge, the variation in the twist results in the buoyancy instability, and subsequent emergence, occurring at different locations along the tube’s length.

The Effect of the Relative Orientation between the Coronal Field and New Emerging Flux. I. Global Properties

The emergence of magnetic flux from the convection zone into the corona is an important process for the dynamical evolution of the coronal magnetic field. In this paper we extend our previous numerical investigations, by looking at the process of flux interaction as an initially twisted flux tube emerges into a plane-parallel, coronal magnetic field. Significant differences are found in the dynamical appearance and evolution of the emergence process depending on the relative orientation between the rising flux system and any preexisting coronal field. When the flux systems are nearly antiparallel, the experiments show substantial reconnection and demonstrate clear signatures of a high-temperature plasma located in the high-velocity outflow regions extending from the reconnection region. However, the cases that have a more parallel orientation of the flux systems show very limited reconnection and none of the associated features. Despite the very different amount of reconnection between the two flux systems, it is found that the emerging flux that is still connected to the original tube reaches the same height as a function of time. As a compensation for the loss of tube flux, a clear difference is found in the extent of the emerging loop in the direction perpendicular to the main axis of the initial flux tube. Increasing amounts of magnetic reconnection decrease the volume, which confines the remaining tube flux.

Structure of magnetic separators and separator reconnection

[1]xa0Magnetic separators are important locations of three-dimensional magnetic reconnection. They are field lines that lie along the edges of four flux domains and represent the intersection of two separatrix surfaces. Since the intersection of two surfaces produces an X-type structure, when viewed along the line of intersection, the global three-dimensional topology of the magnetic field around a separator is hyperbolic. It is therefore usually assumed that the projection of the magnetic field lines themselves onto a two-dimensional plane perpendicular to a separator is also hyperbolic in nature. In this paper, we use the results of a three-dimensional MHD experiment of separator reconnection to show that, in fact, the projection of the magnetic field lines in a cut perpendicular to a separator may be either hyperbolic or elliptic and that the structure of the magnetic field projection may change in space, along the separator, as well as in time, during the life of the separator. Furthermore, in our experiment, we find that there are both spatial and temporal variations in the parallel component of current (and electric field) along the separator, with all high parallel current regions (which are associated with reconnection) occurring between counterrotating flow regions. Importantly, reconnection occurs not only at locations where the structure of the projected perpendicular magnetic field is hyperbolic but also where it is elliptic.

The emergence of toroidal flux tubes from beneath the solar photosphere

Context. Models of flux emergence frequently use a twisted cylindrical loop as the initial starting configuration and ignore the coupling between the radiation field and plasma. In these models, the axis of the original tube never emerges through the photosphere. Without the axis emerging, it is very difficult to form a realistic sunspot. Aims. The aim is to use a toroidal flux loop, placed beneath the solar photosphere and study whether the axis of the system emerges fully into the atmosphere. The toroidal curvature means that the plasma can drain more effectively than in a straight cylindrical tube. Methods. Three-dimensional magnetohydrodynamic numerical simulations of an emerging magnetic flux tube are presented for an initial toroidal loop model. The simulations use a Lagrangian-Remap code that is particularly suited to dealing with shocks and strong current sheets. Results. The evolution of the toroidal loop is followed and the characteristics of the emergence process are compared with the traditional cylindrical loops. The flux sources seen at the photosphere are more circular, and there are less shearing motions in the upper photosphere. When the initial magnetic field strength is relatively weak the evolution of the system is similar to the cylindrical loop case, with the formation of a new flux rope above the photosphere. A striking result is that for large values of field strength the axial field of the toroidal loop emerges fully into the corona. This is reported for the first time in experiments of flux emergence in a highly stratified atmosphere that do not solve self-consistently the radiation transfer problem. In addition, the new flux rope forms below the original axis of the toroidal tube when the field strength is sufficiently strong.

Recursive Reconnection and Magnetic Skeletons

By considering a simple driven model involving the resistive 3D MHD interaction of magnetic sources, it is shown that it is essential to know the magnetic skeleton to determine (1) the locations of reconnection, (2) type of reconnection, (3) the rate of reconnection, and (4) how much reconnection is occurring. In the model, two opposite-polarity magnetic fragments interact in an overlying magnetic field with reconnection, first closing and then opening the magnetic field from the sources. There are two main reconnection phases: the first has one reconnection site at which the flux is closed, and the second has three sites. The latter is a hybrid case involving both closing and reopening reconnection processes. Each reconnection site coincides with its own separator, and hence all reconnection is via separator reconnection. All the separators connect the same two nulls and thus mark the intersection between the same four types of flux domain. In the hybrid state, the two competing reconnection processes (which open and close flux connecting the same two source pairs) run simultaneously, leading to recursive reconnection. That is, the same flux may be closed and then reopened not just once, but many times. This leads to two interesting consequences: (1) the global reconnection rate is enhanced and (2) heating occurs for a longer period and over a wider area than in the single-separator case.

Dynamics of braided coronal loops II: Cascade to multiple small-scale reconnection events

Aims. Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods. The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results. It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this multiple reconnection positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field.

Numerical modelling of 3D reconnection due to rotational footpoint motions

The rapid dynamical evolution of the photospheric magnetic carpet provides a large energy source for the solar corona. In this context, the role of 3D magnetic reconnection is crucial in releasing the free magnetic energy, build up due to the continuous footpoint motions. To understand the processes by which this can take place, we have to obtain a better understanding of the basic reconnection process that can take place in 3D magnetic field configurations. In this paper, we investigate magnetic reconnection, driven by rotational footpoint motions, using 3D numerical MHD simulations. The model consists of two positive and two negative sources, which are placed symmetrically on opposite boundaries of the cubic domain. The initially potential fluxtubes are forced to interact by the rotational driving of the flux concentrations on the boundaries. We consider two variations of this setup, namely with and without an additional, constant, background magnetic field. In the no-background case, the magnetic connectivity is divided into independent regions by separatrix surfaces, while the case with a background field is represented by one global connectivity region. The dynamical evolution is followed and found to differ significantly from the comparable potential evolution. Strong currents are concentrated along separatrix surfaces or rapidly developing quasi-separatrix layers (QSLs). Investigating the reconnection rates of the systems shows that the stronger the background field is, the more efficient the reconnection process of the flux in the respective fluxtubes.

Generalised models for torsional spine and fan magnetic reconnection

Context. Three-dimensional (3D) null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent results from solar observations and from simulations suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. Aims. The properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process – where previous studies always considered a non-generic radially symmetric null. Methods. Analytical solutions are derived for the steady kinematic equations, and are compared with the results of numerical simulations in which the full set of resistive MHD equations is solved. Results. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection occurs in a narrow tube around the spine, with elliptical crosssection when the fan eigenvalues are different. The eccentricity of the ellipse increases as the degree of asymmetry increases, with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased.

Steady state reconnection at a single 3D magnetic null point

Aims. We systematically stress a rotationally symmetric 3D magnetic null point by advecting the opposite footpoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the null point, thereby forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics, which may provide scaling relations for various characteristic parameters of the system. Methods. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The null point is embedded in an initially constant density and temperature plasma. Results. It is shown that a quasi-steady reconnection process can be set up at a 3D null by continuous shear driving. It appears that a true steady state is unlikely to be realised because the current layer tends to grow until it is restricted by the geometry of the computational domain and the imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values, so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic null points.

Numerical modelling of 3D reconnection - II. Comparison between rotational and spinning footpoint motions

The coronal magnetic field is constantly subjected to a variety of photospheric, footpoint motions, leading to the build up, and subsequent release, of magnetic energy. Two different types of footpoint motions are considered here, namely (large scale) rotating and (small scale) spinning, using 3Dxa0numerical MHDxa0simulations. The initial model consists of two aligned, thin flux tubes, which are forced to interact due to the boundary driving of the footpoints. Two variations of this setup are studied, namely with and without an additional, constant, background magnetic field. The nature of the boundary motions determines the shape of the central current sheet, the driving force of the reconnection process, as well as the efficiency of the build up of quasi-separatrix layers (when