Long term variations in solar flare activity

A statistical analysis of the contemporary (1954-1975) solar flare particle events has been made for the parametersF (integrated, proton fluence in cm^-2 in an event with kinetic energy above 10 MeV) andR ₀ (the characteristic rigidity). These data are compared with the long-term averaged values determined from stable- and radio-nuclide measurements of lunar samples. The analysis shows that the ancient solar flare proton spectrum was harder (higher R₀ values) compared to that observed in contemporary flares. A similar analysis can not be made for the mean long-term averaged flux (ˉJ, cm^-2 S^-1), since the contemporary averages suffer from an uncertainty due to the statistics of a single event. However, the average flux estimates for time durations 〈T〉 exceeding 10³ yr, are free from such uncertainties. The long-term averaged ˉJ values obtained over different time scales (10⁴ - 10⁶ yr) suggest a possible periodic variation in solar flare activity, with enhanced flux level during the last 10⁵ yr. The available data rule out the occurrence of giant flares, with proton fluence exceeding 10¹⁵ cm^-2 during the last million years.     

Resonant scattering of particles and second phase acceleration in the solar corona

Solar Physics - Effective acceleration of particles by hydromagnetic turbulence requires that the particles be scattered at a rate ν comparable with the frequency ω of the turbulence. The...     

Long term evolution of solar sector structure

The large-scale structure of the solar magnetic field during the past five sunspot cycles (representing by implication a much longer interval of time) has been investigated using the polarity (toward or away from the Sun) of the interplanetary magnetic field as inferred from polar geomagnetic observations. The polarity of the interplanetary magnetic field has previously been shown to be closely related to the polarity (into or out of the Sun) of the large-scale solar magnetic field. It appears that a solar structure with four sectors per rotation persisted through the past five sunspot cycles with a synodic rotation period near 27.0 days, and a small relative westward drift during the first half of each sunspot cycle and a relative eastward drift during the second half of each cycle. Superposed on this four-sector structure there is another structure with inward field polarity, a width in solar longitude of about 100° and a synodic rotation period of about 28 to 29 days. This 28.5 day structure is usually most prominent during a few years near sunspot maximum. Some preliminary comparisons of these observed solar structures with theoretical considerations are given.     

On the storage of high-energy protons in the solar corona: The cyclotron instability

We consider the problem of long-time storage of high-energy protons, accelerated in the process of a flare, in coronal magnetic traps. From the viewpoint of the storage, one of the most important plasma instabilities is the kinetic cyclotron instability of the Alfvén waves. We carry out a detailed theoretical analysis of the instability for typical conditions of the solar corona. It is the refraction of the Alfvén waves in combination with a drastic decrease of the instability growth rate with an increase of the angle between the directions of the wave vector and the stationary magnetic field that leads to the possibility of the long-term storage of the flare protons. Sufficient conditions of the storage are determined.     

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

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

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.     

Lifetime of solar flare particles in coronal storage regions

Most discussions of lifetime of flare particles in the solar corona have assumed that collision loss is the dominant means of slowing and stopping these particles. The customary formulas used to estimate the rate of collision loss assume individual fast particles interacting with relatively cold matter. However, it is quite possible that the solar cosmic rays are not imbedded in 10⁶ K coronal material but rather all particles in the storage region are energetic. Collision times are sufficiently short so that the energy spectrum may approach a maxwellian distribution with kT on the order of 30 keV. If this is the case, the rate of collision loss will be greatly reduced. Bremsstrahlung and magnetobremsstrahlung then will be the important energy losses. To account for the presence of appreciable numbers of MeV particles, it is probably necessary to postulate the existence of a non-thermal tail in the stored particle distribution.     

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).     

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.     

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.     

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     

Two-fluid model of the solar corona

A simple model of the lower corona which allows for a possible difference in the electron and proton temperatures is analyzed. With the introduction of a phenomenological heating term, temperature and density profiles are calculated for several different cases. It is found that, under certain circumstances, the electron and proton temperatures may differ significantly.     

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.     

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.     

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.     

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.