This review puts together what we have learned about coronal structures and phenomenology to synthesize a physical picture of the corona as a voluminous, thermally and electrically highly-conducting atmosphere responding dynamically to the injection of magnetic flux from below. The synthesis describes complementary roles played by the magnetic heating of the corona, the different types of flares, and the coronal mass ejections as physical processes by which magnetic flux and helicity make their way from below the photosphere into the corona, and, ultimately, into interplanetary space. In these processes, a physically meaningful interplay among dissipative magnetohydrodynamic turbulence, ideal ordered flows, and magnetic helicity determines how and when the rich variety of relatively long-lived coronal structures, spawned by the emerged magnetic flux, will evolve quasi-steadily or erupt with the impressive energies characteristic of flares and coronal mass ejections. Central to this picture is the suggestion, based on recent theoretical and observational works, that the the emerged flux may take the form of a twisted flux rope residing principally in the corona. Such a flux rope is identified with the low-density cavity at the base of a coronal helmet, often but not always encasing a quiescent prominence. The flux rope may either be bodily transported into the corona from below the photosphere, or reform out of a state of flaring turbulence under some suitable constraint of magnetic-helicity conservation. The appeal of this synthesis is its physical simplicity and the manner it relates a large set of diverse phenomena into a self-consistent whole. The implications of this view point are discussed. The topics covered are: the large-scale corona; helmet streamers; quiescent prominences; coronal mass ejections; flares and heating; magnetic reconnection and magnetic helicity; and, the hydromagnetics of magnetic flux emergence.

Solar activity and the corona

The effects of turbulence on magnetic reconnection are investigated by two‐dimensional spectral method magnetohydrodynamic computations. The nonlinear evolution of the periodic sheet pinch configuration is studied as an initial value problem. Turbulence is initiated by including a low level of broadband fluctuations in the initial data. Nonlinear features of the evolution, appropriately described as turbulence, are seen early in the solutions and persist throughout the runs. Small‐scale, unsteady coherent electric current and vorticity structures develop in the reconnection zone, resulting in enhanced viscous and resistive dissipation. Unsteady and often spatially asymmetric fluid flow develops. Large‐scale magnetic islands produced by reconnection activity, undergo internal pulsations. Small‐scale magnetic islands, or ‘‘bubbles’’ develop near the reconnection zone, prodcing multiple X points. Large‐amplitude electric field fluctuations, often several times larger than the reconnection electric field, are produced by large island pulsations and by motion of magnetic bubbles. Spectral analysis of the fluctuations show development of broad band excitations, reminiscent of inertial and dissipation range spectra in homogeneous turbulence. Two‐dimensional spectra indicate that the turbulence is broadband in both spatial directions. It is suggested that the turbulence that develops from the randomly perturbed sheet pinchbears a strong resemblence to homogeneous magnetohydrodynamic turbulence, and that analytical theories of reconnection must incorporate these effects.

Turbulent magnetic reconnection

The Sun's outer atmosphere, or corona, is heated to millions of degrees, considerably hotter than its surface or photosphere. Explanations for this enigma typically invoke the deposition in the corona of nonthermal energy generated by magnetoconvection. However, the coronal heating mechanism remains unknown. We used observations from the Solar Dynamics Observatory and the Hinode solar physics mission to reveal a ubiquitous coronal mass supply in which chromospheric plasma in fountainlike jets or spicules is accelerated upward into the corona, with much of the plasma heated to temperatures between ~0.02 and 0.1 million kelvin (MK) and a small but sufficient fraction to temperatures above 1 MK. These observations provide constraints on the coronal heating mechanism(s) and highlight the importance of the interface region between photosphere and corona.

https://science.sciencemag.org/content/sci/331/6013/55.full.pdf

The Origins of Hot Plasma in the Solar Corona

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.

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

Hydrodynamic and hydromagnetic stability

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

The dynamical conditions that exist when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array are treated. It is shown that in general there is no hydrostatic equilibrium. In place of equilibrium, there is a dynamical nonequilibrium, which leads to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting); this in turn forms tubes of large diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, being dissipated into small-scale motions of the fluid and thence into heat. Referring to the sun, it is pointed out that the twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above.

The rapid dissipation of magnetic fields in highly conducting fluids

The lack of equilibrium in twisted, close-packed flux tubes is demonstrated in terms of a topology of the transverse field and the necessity of defining restricted solutions for an arbitrary function in the equilibrium equation. It is shown that nearly all combinations of flux connections and functional forms have no mutual equilibrium and that the flux connections in nature are formed by footprint convection at an origin. The most close-packed twisted flux tubes are subject to dynamical nonequilibrium, with the transverse flux connections being reduced through neutral point rapid reconnection. The precise solutions which can be obtained through functional forms in the equilibrium equation do not have an analog in the real world.

Absence of equilibrium among close-packed twisted flux tubest

The lines of force of a magnetic field extending through an infinitely conducting fluid between footpoints on the planes z=0 and z=L can be wrapped and interwoven by bounded continuous motions of the footpoints into a random sequence of arbitrary topological patterns along the field. The sign of the topological helicity of the winding pattern of the field vanes at random along the field. On the other hand, in force-free equilibrium the relative helicity (α=B. ▿ B/B 2) is rigorously constant along each line of force. Indeed in the limit of an endless random sequence of independent winding patterns along the field, the helicity falls asymptotically to zero and the field becomes curl free. A field with constant helicity along each line of force is obliged to create internal tangential discontinuities (in which the sign of the curl and the helicity is arbitrary) if it is to follow the varying topological helicity imposed by the twists and turns of the succession of independent winding patterns.

Spontaneous tangential discontinuities and the optical analogy for static magnetic fields. I. Force-free fields, potential fields, and discontinuities

The properties of Alfven waves propagating along a uniform horizontal field in a highly conducting incompressible medium in the presence of strong convective instability are examined in the Boussinesq approximation. In particular, it is sought to determine whether there are exact solutions to the dynamical equations in the presence of convective forces. It is shown that a class of exact solutions of arbitrary amplitude, but of limited form, which may be of some physical interest, does exist. For large amplitudes, any mixtures of polarization states are shown to cause scattering into new modes.

E. N. Parker

Papers

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

The rapid dissipation of magnetic fields in highly conducting fluids

Absence of equilibrium among close-packed twisted flux tubest

Spontaneous tangential discontinuities and the optical analogy for static magnetic fields. I. Force-free fields, potential fields, and discontinuities

Alfven waves in a thermally stratified fluid