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.     

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.     

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).     

A piston-driven shock in the solar corona

A solar flare that occurred on the west limb at 1981, March 25, 2038 UT generated a massive, rapidly-expanding optical coronal transient, which moved outward with an approximately constant velocity of 800 km s^–1. An associated magnetohydrodynamic shock travelled out ahead of the transient with a velocity estimated to be approximately 1000 km s^–1. The optical and radio data on the transient and shock fit well with general theories concerning piston-driven shocks and with current MHD models for propagation of such shocks through the solar corona.     

Gas-magnetic field interactions in the solar corona

It is evident from eclipse photographs that gas-magnetic field interactions are important in determining the structure and dynamical properties of the solar corona and interplanetary medium. Close to the Sun in regions of strong field, the coronal gas can be contained within closed loop structures. However, since the field in these regions decreases outward rapidly, the pressure and inertial forces of the solar wind eventually dominate and distend the field outward into interplanetary space. The complete geometrical and dynamical state is determined by a complex interplay of inertial, pressure, gravitational, and magnetic forces. The present paper is oriented toward the understanding of this interaction. The helmet streamer type configuration with its associated neutral point and sheet currents is of central importance in this problem and is, therefore, considered in some detail.Integration of the relevant partial differential equations is made tractable by an iterative technique consisting of three basic stages, which are described at length. A sample solution obtained by this method is presented and its physical properties discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Geometrical considerations in imaging the solar corona

X-ray observations of the solar corona show that it is comprised of three-dimensional magnetic structures which appear to be primarily in the form of fluxtubes or loops. Imaging the X-ray corona has led to a greater understanding of the dynamical behaviour of and the energy distribution in these magnetic structures. However, imaging observations, by their very nature, integrate along the line of sight resulting in a two-dimensional representation of the actual three-dimensional distribution. The optically thin nature of the solar corona to X-ray radiation makes the integrated images particularly difficult to interpret. The analysis of the two-dimensional observations must, therefore, inlcude the effect of the orientation of the coronal structure to the line-of-sight direction; a fact which is almost always ignored. In this paper we discuss the effect of loop orientation on the two-dimensional representation and argue that these effects may lead to a misinterpretation of the physics occurring in the structures observed. In particular, we discuss observations taken by the Soft X-ray Telescope (SXT) on board the Yohkoh satellite, taking account of the instrumental thermal response, spatial resolution, and point-spread-function.We test the effect of geometry on the determination of the loop pressure by considering equatorial loops at various longitudes and discuss the implications of this for studies of coronal soft X-ray loops.     

Two-dimensional MHD equilibria in the solar corona

Using a combined analytical and numerical Method we have treated the question of two-dimensional MHD equilibriam in an inviscid compressible, perfect conducting plasma with an embedded magnetic field in the spherically symmetric gravitational field of the sun. Two solutions are obtained. (1) A steady, self-consistent plasma flow in a magnetic field with both a closed and an open region. In the open region, beyond a few solar radii, the plasma velocity exceeds the local sound and Alfvén velocities. (2) The plasma velocity is everywhere smaller than the local sound and Alfvén velocities and tends to zero at large radial distances.     

Multiple radio echoes in the solar corona

Echo-type solar radio bursts are associated with preceding short-lived bursts in double events. The peculiar and rather rare decameter echoes are observed with a UTR-2 antenna. The initial narrow-band burst is followed, some 5 to 10 s later, by an echo-like burst at the same frequency. The observational data obtained for decameter echo evens are, on the whole, consistent with the model of a pulsed source emitting radio signals at the plasma-frequency harmonic, which is placed in a non-uniform corona and rotates together with the Sun.Intensity-time profiles of 25 MHz echo bursts are of an unusual shape, featuring an extended leading edge and an abrupt decay at the trailing edge and also showing some fine structures in the form of an additional, weakly pronounced maximum or a step at the final stage of the burst. Time parameters characterizing the profiles are evaluated. The step is delayed with respect to the main pulse at about two times longer than the principal echo maximum. At the same time, the time delays depend essentially on the heliolongitude of the active region and achieve their maximum values at the meridian. The step height does not exceed 0.5 of the echo maximum. At this level, the echo-decay time almost coincides with the initial burst duration but is about 1.7 times less than the echo-rise time. The feature at the echo tail can be interpreted as a result of a repeated reflection of the burst from the source region. The causes and conditions for the formation of multiple echoes are discussed. The extended leading edge of the echo permits us to assume a quasi-radial fibrous structure of the corona, capable of back-scattering the incident radiation.     

Bulk flow velocities in the solar corona

We present velocity estimates of bulk motions in the solar corona using data from the Large Angle Spectrometric Coronagraph (LASCO) aboard the Solar and Heliospheric Observatory spacecraft ( SOHO ). We describe a new technique which automatically provides a mass-weighted mean velocity profile in an entirely objective fashion without the need for individual event identification. A weighted velocity profile of this kind reflects the motion of the energetically dominant component of the coronal mass ejection (CME) mass spectrum and is of particular interest in consideration of the overall energy budget of the CME process. We consider the mean motion within three latitudinal bands centred at 0°, 20° and 40° over a one-year period around the time of solar minimum. We find terminal velocities within the LASCO field of around 300 km s⁻¹ in all latitude bands but note a latitudinal dependence in CME evolution through the low corona prior to reaching these velocities. We find evidence that ejections in the equatorial zone undergo continuous acceleration whilst at higher latitudes a discrete burst of acceleration is seen to occur at around 4 R_⊙ from the Sun's centre with relatively little acceleration thereafter. We also consider the energy deposition rates necessary to generate these profiles.     

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.     

Magnetic polarimetric refraction in the solar corona

We present expressions which describe the angular displacement of radio sources due to refraction in a magnetized plasma. The main objective of the present paper is to take into account the combined effect of gradients of the electron density and the magnetic field. We use the geometrical optics approximation for the determination of the angular broadening of the radiation. The expressions obtained are applied to the case of the solar corona.     

Electron-cyclotron heating of the solar corona

A model of heating of the solar corona is proposed using electron-cyclotron resonance heating.     

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     

On the temperature distribution in the solar corona

An improved value of coronal temperature is obtained by the degree of ionization method taking various processes into consideration. Comparison with some of the existing results has also been made.     

Time-dependent heating of the solar corona

The problem of how the corona is heated is of central importance in solar physics research. Here it is assumed that the heating occurs in a regular time-dependent manner and the response of the plasma is investigated. If the magnetic field is strong then the dynamics reduces to a one-dimensional problem along the field. In addition if the radiative time in the corona is much longer than the sound travel time then the plasma evolvesisobarically. The frequency with which heat is deposited in the corona is investigated and it is shown that there is a critical frequency above which a hot corona can be maintained and below which the plasma temperature cools to chromospheric values. An evaluation of the isobaric assumption to the solar corona and the implications of time-dependent heating upon the forthcoming SOHO observations are also presented.     

Radiative origins of the solar corona

Within observational accuracy, the radiation pressure 1/3aT ⁴ at the effective solar temperature is equal to the coronal gas pressurenkT. This suggests a radiative-gas discontinuity between optically thick and optically thin regions. Ideal transitions of this nature are studied and the applicability of this model to the Sun is explored. Further empirical corroboration is obtained if the gas pressure anomalies of Gulyaev are resolved by postulating a corrective gradient of radiation pressure possibly caused by Lyman- opacity.