Klaus Galsgaard

Heating and activity of the solar corona: 1. Boundary shearing of an initially homogeneous magnetic field

To contribute to the understanding of heating and dynamic activity in boundary-driven, low-beta plasmas such as the solar corona, we investigate how an initially homogeneous magnetic field responds to random large-scale shearing motions on two boundaries, by numerically solving the dissipative MHD equations, with resolutions ranging from 24 3 to 136 3 . We find that even a single application of large-scale shear, in the form of orthogonal sinusoidal shear on two boundaries, leads to the formation of tangential discontinuities (current sheets). The formation time scales logarithmically with the resistivity and is of the order of a few times the inverse shearing rate for any reasonable resistivity, even though no mathematical discontinuity would form in a finite time in the limit of vanishing resistivity. The reason for the formation of the current sheets is the interlocking of two magnetic flux systems. Reconnection in the current sheets is necessary for the field lines to straighten out. The formation of current sheets causes a transition to a very dynamic plasma state, where reconnection drives supersonic and super-Alfvenic jet flows and where these, in turn, cause the formation of smaller-scale current sheets. A statistically steady state level for the average Poynting flux and the average Joule dissipation is reached after a few correlation times, but both boundary work and Joule dissipation are highly fluctuating in time and space and are only weakly correlated. Strong and bursty Joule dissipation events are favored when the volume has a large length/diameter ratio and is systematically driven for periods longer than the Alfven crossing time. The understanding of the reason for the current sheet formation allows a simple scaling law to be constructed for the average boundary work. Numerical experiments over a range of parameter values, covering over 3 orders of magnitude in average dissipation, obey the scaling law to within a factor of 2. The heating rate depends on the boundary velocity amplitude and correlation time, the Alfven speed, and the initial magnetic field strength but appears to be independent of the resistivity because of the formation of a hierarchy of current sheets. Estimates of the photospheric boundary work on the solar coronal magnetic field using the scaling law are consistent with estimates of the required coronal heating rates. We therefore conclude that the work supplied to the solar corona as a consequence of the motion of the magnetic foot points in the solar photosphere and the emergence of new flux is a significant contributor to coronal heating and flaring and that it quite plausibly is the dominant one.

Jets in Coronal Holes: Hinode Observations and Three-dimensional Computer Modeling

Recent observations of coronal hole areas with the XRT and EIS instruments on board the Hinode satellite have shown with unprecedented detail the launching of fast, hot jets away from the solar surface. In some cases these events coincide with episodes of flux emergence from beneath the photosphere. In this Letter we show results of a three-dimensional numerical experiment of flux emergence from the solar interior into a coronal hole and compare them with simultaneous XRT and EIS observations of a jet-launching event that accompanied the appearance of a bipolar region in MDI magnetograms. The magnetic skeleton and topology that result in the experiment bear a strong resemblance to linear force-free extrapolations of the SOHO/MDI magnetograms. A thin current sheet is formed at the boundary of the emerging plasma. A jet is launched upward along the open reconnected field lines with values of temperature, density, and velocity in agreement with the XRT and EIS observations. Below the jet, a split-vault structure results with two chambers: a shrinking one containing the emerged field loops and a growing one with loops produced by the reconnection. The ongoing reconnection leads to a horizontal drift of the vault-and-jet structure. The timescales, velocities, and other plasma properties in the experiment are consistent with recent statistical studies of this type of event made with Hinode data.

The Three-dimensional Interaction between Emerging Magnetic Flux and a Large-Scale Coronal Field: Reconnection, Current Sheets, and Jets

Using MHD numerical experiments in three dimensions, we study the emergence of a bipolar magnetic region from the solar interior into a model corona containing a large-scale, horizontal magnetic field. An arch-shaped concentrated current sheet is formed at the interface between the rising magnetized plasma and the ambient coronal field. Three-dimensional reconnection takes place along the current sheet, so that the corona and the photosphere become magnetically connected, a process repeatedly observed in recent satellite missions. We show the structure and evolution of the current sheet and how it changes in time from a simple tangential discontinuity to a rotational discontinuity with no null surface. We find clear indications that individual reconnection events in this three-dimensional environment in the advanced stage are not one-off events, but instead take place in a continuous fashion, with each field line changing connectivity during a finite time interval. We also show that many individual field lines of the rising tube undergo multiple processes of reconnection at different points in the corona, thus creating photospheric pockets for the coronal field. We calculate global measures for the amount of subphotospheric flux that becomes linked to the corona during the experiment and find that most of the original subphotospheric flux becomes connected to coronal field lines. The ejection of plasma from the reconnection site gives rise to high-speed and high-temperature jets. The acceleration mechanism for those jets is akin to that found in previous two-dimensional models, but the geometry of the jets bears a clear three-dimensional imprint, having a curved-sheet appearance with a sharp interface to the overlying coronal magnetic field system. Temperatures and velocities of the jets in the simulations are commensurate with those measured in soft X-rays by the Yohkoh satellite.

Heating and activity of the solar corona: 3. Dynamics of a low beta plasma with three-dimensional null points

We investigate the self-consistent nonlinear evolution of an initially force-free three-dimensional magnetic field subjected to stress on two boundaries. The results illustrate how complicated magnetic field structures, such as those found in the solar corona, evolve dynamically when forced by stress from boundaries and how the energy which is temporarily stored in the magnetic field may be converted into other forms of energy such as heat, flow energy, and fast particles. The initial model state is triple periodic and contains eight magnetic null points. During the time evolution, the current density concentrates near particular locations in space that can be identified with the singular field lines connecting pairs of null points of the initial state. Current sheets are found to grow out of the singular lines formed by the intersection of surfaces across which the magnetic connectivity is discontinuous. Jets of plasma shoot out from the edges of the currents sheets, driven by the “sling-shot” Lorentz force created by reconnecting magnetic field lines. As a result of the reconnection, most of the magnetic connectivity between the two boundaries is lost, and the remaining magnetic field develops arcade-like structures along the boundaries. These arcade structures are long-lived, and the system enters a quasi-stationary state, where small-scale current sheets are continually appearing and disappearing. The distribution of size of these current sheets is limited only by the numerical resolution. The current sheets dissipate the energy supplied by the boundary driving and also slowly deplete the magnetic energy from the initial constant alpha magnetic field. The dissipation occurs in an increasing number of current sheets of decreasing size at higher numerical resolution, which keeps the overall reconnection rate nearly independent of the numerical resolution. This suggests that “fast reconnection” may occur through the collaborative effort of a large number of many small-scale current sheets, rather than in the very large magnetic Reynolds number limit of single current sheets that has been so extensively discussed in the literature. This has important applications to both the problem of understanding coronal heating and the search for efficient flare energy release mechanisms.

Plasma Jets and Eruptions in Solar Coronal Holes: A Three-dimensional Flux Emergence Experiment

A three-dimensional (3D) numerical experiment of the launching of a hot and fast coronal jet followed by several violent eruptions is analyzed in detail. These events are initiated through the emergence of a magnetic flux rope from the solar interior into a coronal hole. We explore the evolution of the emerging magnetically dominated plasma dome surmounted by a current sheet and the ensuing pattern of reconnection. A hot and fast coronal jet with inverted-Y shape is produced that shows properties comparable to those frequently observed with EUV and X-ray detectors. We analyze its 3D shape, its inhomogeneous internal structure, and its rise and decay phases, lasting for some 15-20?minutes each. Particular attention is devoted to the field line connectivities and the reconnection pattern. We also study the cool and high-density volume that appears to encircle the emerged dome. The decay of the jet is followed by a violent phase with a total of five eruptions. The first of them seems to follow the general pattern of tether-cutting reconnection in a sheared arcade, although modified by the field topology created by the preceding reconnection evolution. The two following eruptions take place near and above the strong-field concentrations at the surface. They show a twisted, ?-loop-like rope expanding in height, with twist being turned into writhe, thus hinting at a kink instability (perhaps combined with a torus instability) as the cause of the eruption. The succession of a main jet ejection and a number of violent eruptions that resemble mini-CMEs and their physical properties suggest that this experiment may provide a model for the blowout jets recently proposed in the literature.

A three-dimensional study of reconnection, current sheets, and jets resulting from magnetic flux emergence in the sun

We present the results of a set of three-dimensional numerical simulations of magnetic flux emergence from below the photosphere and into the corona. The corona includes a uniform and horizontal magnetic field as a model for a preexisting large-scale coronal magnetic system. Cases with different relative orientations of the upcoming and coronal fields are studied. Upon contact, a concentrated current sheet with the shape of an arch is formed at the interface that marks the positions of maximum jump in the field vector between the two systems. Relative angles above 90° yield abundant magnetic reconnection and plasma heating. The reconnection is seen to be intrinsically three-dimensional in nature and to be accompanied by marked local heating. It generates collimated high-speed outflows only a short distance from the reconnection site, and these propagate along the ambient magnetic field lines as jets. As a result of the reconnection, magnetic field lines from the magnetized plasma below the surface end up connecting to coronal field lines, thus causing a profound change in the connectivity of the magnetic regions in the corona. The experiments presented here yield a number of features repeatedly observed with the TRACE and Yohkoh satellites, such as the establishment of connectivity between emergent and preexisting active regions, local heating, and high-velocity outflows.

Particle acceleration in stochastic current sheets in stressed coronal active regions

Aims. To perform numerical experiments of particle acceleration in the complex magnetic and electric field environment of the stressed solar corona. Methods. The magnetic and electric fields are obtained from a 3-D MHD experiment that resembles a coronal loop with photospheric regions at both footpoints. Photospheric footpoint motion leads to the formation of a hierarchy of stochastic current sheets. Particles (protons and electrons) are traced within these current sheets starting from a thermal distribution using a relativistic test particle code. Results. In the corona the particles are subject to acceleration as well as deceleration, and a considerable portion of them leave the domain having received a net energy gain. Particles are accelerated to high energies in a very short time (both species can reach energies up to 100 GeV within 5 × 10 −2 s for electrons and 5 × 10 −1 s for protons). The final energy distribution shows that while one quarter of the particles retain their thermal distribution, the rest have been accelerated, forming a two-part power law. Accelerated particles are either trapped within electric field regions of opposite polarities, or escape the domain mainly through the footpoints. The particle dynamics are followed in detail and it is shown how this dynamic affects the time evolution of the system and the energy distribution. The scaling of these results with time and length scale is examined and the Bremstrahlung signature of X-ray photons resulting from escaping particles hitting the chromosphere is calculated and found to have a main power law part with an index γ = −1.8, steeper than observed. Possible resolutions of this discrepency are discussed.

Heating and activity of the solar corona: 2. Kink instability in a flux tube

The development of kink instability in a flux tube is investigated numerically, by solving the resistive MHD equations in three dimensions for a setup where a flux tube is stressed by rotating both ends in opposite directions. Two cases are investigated: one where the tube is initially isolated and in pressure equilibrium with surrounding plasma (external kink) and another with an initially uniform magnetic field, where only a smaller part of the boundaries are used to twist the field (internal kink). The twist angle at the onset of the kink instability depends on several parameters, such as rotation velocity, tube diameter, field strength, and magnetic resistivity, but is generally in the range 4π–8π. Both sets of experiments are followed beyond the point where they become kink unstable into the regime of nonlinear evolution. Of particular interest is the topological evolution. As magnetic dissipation becomes significant, the connectivity between the two boundaries changes from ordered to chaotic, and small-scale current sheets develop. Even though the gross features of the external kink appear to saturate, the total magnetic energy continues to grow, by a steady increase of the free energy in the chaotic region that develops as a result of the kink and by a secular spreading of the magnetic field into the initially field-free region. The internal kink is confined to the cylinder defined by the boundary driving and has only limited influence on the external magnetic field. After the kink, the twist of the magnetic field is reduced, and the internal kink settles into a quasi-steady state where the dissipation on the average balances the Poynting flux input. The average Poynting flux is similar in the external and internal kinks, with a magnitude that corresponds to local winding numbers of the order of unity. Scaling of these results to values characteristic of the solar corona indicate that systematic rotation or shear of the endpoints could be a source of quasi-steady heating in coronal loops.

Magnetohydrodynamic evolution of magnetic skeletons

The heating of the solar corona is probably due to reconnection of the highly complex magnetic field that threads throughout its volume. We have run a numerical experiment of an elementary interaction between the magnetic field of two photospheric sources in an overlying field that represents a fundamental building block of the coronal heating process. The key to explaining where, how and how much energy is released during such an interaction is to calculate the resulting evolution of the magnetic skeleton. A skeleton is essentially the web of magnetic flux surfaces (called separatrix surfaces) that separate the coronal volume into topologically distinct parts. For the first time, the skeleton of the magnetic field in a three-dimensional numerical magnetohydrodynamic experiment is calculated and carefully analysed, as are the ways in which it bifurcates into different topologies. A change in topology normally changes the number of magnetic reconnection sites. In our experiment, the magnetic field evolves through a total of six distinct topologies. Initially, no magnetic flux joins the two sources. Then, a new type of bifurcation, called a global double-separator bifurcation, takes place. This bifurcation is probably one of the main ways in which new separators are created in the corona (separators are field lines at which three-dimensional reconnection takes place). This is the first of five bifurcations in which the skeleton becomes progressively more complex before simplifying. Surprisingly, for such a simple initial state, at the peak of complexity there are five separators and eight flux domains present.

ON THE NATURE OF RECONNECTION AT A SOLAR CORONAL NULL POINT ABOVE A SEPARATRIX DOME

Three-dimensional magnetic null points are ubiquitous in the solar corona and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spine-fan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasi-separatrix layer or slip-running reconnection.