The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

The solar X-ray corona

The solar corona, and the coronae of solar-type stars, consist of a low-density magnetized plasma at temperatures exceeding 10⁶ K. The primary coronal emission is therefore in the UV and soft x-ray range. The observed close connection between solar magnetic fields and the physical parameters of the corona implies a fundamental role for the magnetic field in coronal structuring and dynamics. Variability of the corona occurs on all temporal and spatial scales—at one extreme, as the result of plasma instabilities, and at the other extreme driven by the global magnetic flux emergence patterns of the solar cycle.     

The solar wind and the temperature-density structure of the solar corona

The influence of the solar wind on large-scale temperature and density distributions in the lower corona is studied. This influence is most profoundly felt through its effect upon the geometry of coronal magnetic fields since the presence of expansion divides the corona into magnetically open and closed regions. Each of these regions is governed by entirely different energy transport processes. This results in significant temperature differences since only the open field regions suffer outward conductive heat losses. Because the temperature influences the density in an exponential manner, large density inhomogeneities are to be expected.An approximate method for calculating the temperature and density distribution in a known magnetic field geometry is outlined and numerical estimates are carried out for representative coronal conditions. These estimates show that temperature differences of a factor of about two and density differences of ten can be expected in the lower corona even for uniform base conditions. As a result, we do not regard the so-called coronal holes necessairly as locations of reduced mechanical heating. Alternatively, we suggest that they are regions of open magnetic field lines being continuously drained of energy contert by the solar wind expansion and outward thermal conduction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The spectrum of Nixix in the solar corona

The wavelengths and intensities of the stronger transitions in the spectrum of Ni xix are reduced from measurements of the X-ray spectra of three coronal active regions. The new measured wavelengths are consistent with prediction by isoelectronic extrapolation from the wavelengths of well established transitions but are about 0.01 Å longer than previously accepted laboratory measurements. This difference appears to be crucial to the correct assignment of features in the coronal spectrum to Ni xix. The relative intensities of our new assignments to Ni xix are in broad agreement with the Loulergue-Nussbaumer calculations.     

Electrons in the solar corona

We discuss a model for the formation of the chromospheric Ca ii K line which does not make the usual assumption of complete redistribution. Using a physically reasonable scattering model, we find significant departures due to the frequency dependence of the line source function, particularly in the relative intensity and centre-to-limb behaviour of the K₁ parts of the line and in the asymmetry produced by differential velocity fields. We conclude that the frequency dependence of the K line source function must be considered in quantitative models for the formation of the K line.     

Electrons in the solar corona

During a balloon flight in France on September 13, 1971, at altitude 32 000 m, the solar corona was cinematographed from 2 to 5R during 5 hr, with an externally occulted coronagraph.Motions in coronal features, when they occur, exhibit deformations of structures with velocities not exceeding a few 10 km s^–1; several streamers were often involved simultaneously; these variations are compatible with magnetic changes or sudden reorganizations of lines of forces.Intensity and polarization measurements give the electron density with height in the quiet corona above the equator. Electron density gradient for one of the streamers gives a temperature of 1.6 × 10⁶ K and comparisons with the on-board Apollo 16 coronal observation of 31 July, 1971 are compatible with the extension of this temperature up to 25 R _bd.Three-dimensional structures and localizations of the streamers are deduced from combined photometry, polarimetry and ground-based K coronametry. Three of the four coronal streamers analysed have their axis bent with height towards the direction of the solar rotation, as if the upper corona has a rotation slightly faster than the chromosphere.     

Electrons in the solar corona

The polarimetric survey of electrons in the K-corona initiated at Pic-du-Midi and Meudon Observatories in 1964 now covers a full solar cycle of activity. The measurements are photometrically calibrated in an absolute scale.In June 1967 a persistent coronal feature was fan-shaped as a lame coronale above quiescent prominences. We deduce an electron density of N ₀ = 1.5 × 10⁸ at 60 000 km above the photosphere, a total number of 14 × 10³⁹ electrons, a hydrostatic temperature of 1.7 × 10⁶ K, and a total thermal energy 3N _eKT = 1.0 × 10³¹ ergs. When a center of activity appeared, a major localized condensation developed to replace the old elongated feature, with N ₀ = 4.5 × 10⁸, a total of 4.5 × 10³⁹ electrons and the same temperature of 1.7 × 10⁶ K.Also, a fan-shaped feature of exceptional intensity was analysed on 8 September 1966, with N ₀ = 6 × 10⁸ and a total of 24 × 10³⁹ electrons.Fan-shaped features are frequent above quiescent prominences. They degenerate above a height of 2R into thinner isolated columns or blades with temperatures also around 1.7 × 10⁶ K.     

The propagation of electron fluxes in the solar corona

The problem of energetic electron flux propagation in the solar coronal plasma is solved with due regard for the influence of the oppositely directed neutralizing cold electron flux and the kinematic escape effect of the electrons with different velocities. It is shown that the flux electrons are accelerated in the process of propagation, thus forming a beam, whose velocity is constant on rather long time scales. Three regimes can be realized in this case. In the first regime, plasma waves do not have time to be excited because they escape rapidly from resonance with the beam. In the second regime, waves are excited, but the beam does not have time to relax. The third regime is quasi-linear relaxation.The generation of solar type III radio bursts in the second regime of electron flux propagation is considered.     

Heating of the solar corona

The suggestion is advanced that heating of the solar corona results from Landau damping of ion-acoustic waves generated in the motion of photospheric granules. Laboratory experiments relevant to the question of corona heating are discussed, together with the available observational information on the extent of energy deposition in the corona.Of the European Space Research Organization (ESRO).     

The solar corona: Flat formation

During the greater part of the 11-year sunspot cycle the solar corona represents largely a similar flat formation as in the minimum (looking like a galaxy), The observed variety of coronal forms is mainly due to variations of the corona's orientation as seen from the Earth. Two limiting cases of coronal orientation are discussed: perpendicular to the plane of the sky (edgewise towards the observer) and parallel with the plane of the sky. The first case is illustrated with the coronal observations of 11 July, 1991. The second case provides an opportunity to observe the corona from above the solar magnetic poles.     

The corona associated with solar filaments

Spectroheliograms in high temperature ions such as Fe XV show the existence of both filaments that are brighter than the ambient corona and filaments that are darker than the ambient corona. We describe the relationship of the filaments to photospheric magnetograms, and discuss a possible physical mechanism to explain the differences.     

The green corona,the solar wind and geoactivity

The long-term distribution of the Green Corona Low Brightness Regions (GCLBR) on the solar surface is investigated. The frequency curves of the GCLBR follow the solar cycle, but are displaced considerably relative to the curve of the sunspot number cycle. The observed displacement increases with the size of the GCLBR and reaches up to 4–5 years for the largest regions. It is, however, interesting that the displacement in the equatorial zone is opposite to that in the higher-latitude zones.An older idea on the physical affinity between GCLBR and coronal holes led us to study the frequency of GCLBR and the properties of High-Speed Plasma Streams (HSPS) in the solar wind. Maximum velocity and duration of the coronal-hole-related HSPS seem to be well correlated with the number and size of GCLBR located in the N 60-N 20 and S 20-S 60 latitudinal zones. This is particularly evident at the end of the solar cycle.Geophysical Kp and aa indices are used to demonstrate a possible genetic dependence of geoactivity on the size, position on the Sun's surface and frequency of the GCLBR. In this sense, the most pronounced period is 1973–1976.

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Siphon flows in the solar corona

The flows in a coronal magnetic arch associated with a pressure difference between the footpoints are investigated. Steady flows are of different types: always subsonic; subsonic in one branch of the arch, supersonic in the second; subsonic-supersonic with stationary shocks which adjust the flow to the boundary conditions in the second footpoint. The large velocity increase along the loop in subsonic-supersonic flows is associated with a large density decrease. A velocity drop and a density jump occur across the shock. The emission of such arches in coronal lines (625 of Mg x and 499 of Si xii) is calculated. It is suggested that the intensity drop along the axis observed in some UV loops is due to the density drop associated with subsonic-supersonic flows.     

The colour of the solar corona and dust grains in it

The photometry of coronal colour negatives is carried out. The films were obtained at the March 7, 1970 and July 10, 1972 eclipses. A distribution of the coronal brightness in the red (635 nm), green (545 nm), and blue (455 nm) wavelength intervals up to distances of (6–7)R is deduced (Figure 1). Colour indexes of the corona (the emission ratio red/blue - C _rb and green/blue - C _gb) have been obtained. We assume C _rb = C _gb = 1 in the inner corona (2R ). The maximum of colour indexes of the 1970 corona are at the distances of about 4R (C _rb 1.9 and C _gb 1.7). A slight reddening within the limits of the errors was found in the 1972 corona.There is a correlation between colour indexes and diffuse external reinforcements (RED) brightness. The analysis of the results leads to the conclusion that RED consists of dust grains with radii 1 m. RED brightness is evaluated to be 4 × 10^-10 B . There is 1 grain of dust in the elementary volume with cross section of 1 cm² along the line of sight. The intensity of dust emission in wavelength interval 10 m deduced by the authors is approximately 1 W cm^-2 s m^–1. That is in agreement with Mankin et al. (1974) and Léna et al. (1974) observations. The whole dust mass of RED is 1% of the coronal gas mass contained within RED region. The dust grain number density is about 10^-11 cm^-3.Determinations of the colour of the solar corona have been made by a number of scientists (Tikhov, 1940, 1957; Allen, 1946; Blackwell, 1952; Michard, 1956; Sharonov, 1958; Nay et al., 1961). The corona colour was found to be somewhat redder than the Sun's. However this question is not finally settled to date.     

Plasma drift in the solar corona

Model calculations of plasma drifts in the solar corona were performed. We established that only drifts in crossed fields could result in velocities V of several hundred kilometers per second. Such velocities are typical of coronal mass ejections (CMEs). We derived an analytic expression for V where n, the expansion harmonic of the magnetic-field strength, varies with time. As follows from this expression, V is a power function of the distance with index (2?n) and the radial component changes sign (n?1) times in the latitude range from ?π/2 to +π/2. We found that if the magnetic dipole moment varies with time, the similarity between the spiral structures of coronal plasma is preserved when they displace within several solar radii and the density gradient at the conical boundaries increases (the apparent contrast is enhanced). There is a correspondence between the inferred model effects and the actually observed phenomena that accompany CMEs.     

The stability of electron beams in the flaring solar corona

The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission.     

The cooling of flare produced plasmas in the solar corona

Solar flare X-rays, at energies less than 10 keV, are emitted by hot plasmas located in the corona. Three plasma cooling models are examined in detail. The cooling of the electrons by Coulomb collisions with ions at a lower temperature would require the observed material to occupy very large volumes. Cooling could take place by conduction or by radiation and observations are proposed which would allow the dominant cooling mechanism to be established.On leave during a portion of this work as University Research Fellow in Astronomy, University of Leicester, England.     

Nanoflares and heating of the solar corona

Coronal heating by nanoflares is presented by using observational, analytical, numerical simulation and statistical results. Numerical simulations show the formation of numerous current sheets if the magnetic field is sheared and bipoles have unequal pole strengths. This fact supports the generation of nanoflares and heating by them. The occurrence frequency of transients such as flares, nano/microflares, on the Sun exhibits a power-law distribution with exponent α varying between 1.4 and 3.3. For nanoflares heating α must be greater than 2. It is likely that the nanoflare heating can be reproduced by dissipating Alfven waves. Only observations from future space missions such as Solar-B, to be launched in 2006, can shed further light on whether Alfven waves or nanoflares, heat the solar corona.