MHD waves in coronal flux tubes

The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona.     

Morphology and physics of short-period magnetic pulsations

This review is devoted to the main problems of experimental and theoretical investigations of geoelectromagnetic waves in the frequency range from 0.1 to 5 Hz. These waves constitute the short-period subclass of so-called geomagnetic pulsations. The short-period pulsations are represented by Pc1, Pc2, Pi1, Ipdp types and some subclassifications. The understanding of the pulsation mechanisms provides an insight into the structure and dynamics of the Earth's magnetosphere. We focus our attention on Pc1 pearl pulsations and on the classical (evening) Ipdp, for which basic physical concepts have been established. Other types and varieties are outlined also, but in less detail. In these cases, the physical mechanism is not always clear (as, for example, in the case of morning Ipdp), and/or the morphology is still to be determined carefully (Pc2 and discrete signals in polar cusps as typical examples).Short-period pulsations are a spontaneous, sporadic phenomenon which undergo a certain evolution in the course of a magnetic storm. We consider the storm-time variation as a natural background, and we use this background to collect the information about the pulsations in an orderly manner. At the same time, together with the transient storm-time variation of pulsation activity, quasi-periodic variations take place, which are connected with the Earth's and Sun's rotation, Earth's orbital motion and solar cycle activity. The study of these regular variations allows us to have a new approach to the mechanisms of excitation and propagation of short-period geomagnetic pulsations.     

Models of coronal hole flows

Models of plasma flow in a coronal hole fall naturally into four classes. These are: (i) radial flow on a streamline along which the divergence is assumed to vary differently than as the square of the radial distance from the Sun; (ii) global flow along streamlines determined in some independent manner; (iii) empirical models originating in, or based strongly on observation; (iv) dynamic models using magnetic and plasma boundary conditions low in the corona to find both the geometry of streamlines and the flow field.To date, models both of ideal coronal holes and of specific observed coronal holes indicate that flow velocities above 100 km s⁺¹, and temperatures of perhaps 2 × 10⁶K are possible at 2R heliocentric distance, where densities of 2 × 10⁵ cm⁺³ have been reported. These velocities are at, or just above the sound speed, although still sub-Alfvénic. There is also general agreement among models of large polar holes that conversion of mechanical wave energy flux into solar wind kinetic energy is occurring in the 2R to 5R range, perhaps occurs even further outwards, and that the magnitude and extent of this energy deposition depends on the size and on the geometrical divergence of the hole.However, each model exhibits distinct weaknesses counteracted only by the complimentary nature of the various types of models. Models in class (i) are simply not global representations, but are tractable when dealing with complex forms of the energy equation or with several ion species. Class (ii) models lack any geometrical information beyond the ad hoc assumption of known streamline geometry, but have the same advantages as those in class (i). Class (iii) models cannot determine streamline geometry within a hole and do not extend further from the Sun than the available data — although they place important constraints on models in the other classes. Class (iv) models are limited to simple forms of the energy equation and/or to quasi-radial flow, but are the only models producing self-consistent streamline geometries through inclusion of transverse magnetic stresses in the momentum equation.Most limitations in coronal hole flow models can be eliminated by using known numerical techniques to combine models in classes (i), (ii), and (iv). This would allow detailed models of coronal holes and corresponding interplanetary conditions to be developed for specific time periods, at the cost of flexibility and possibly also general conceptual understanding. Nevertheless, the concept of a coronal hole is now reasonably well established, and acceptable modelling approaches are rapidly filling the literature. It can be anticipated that the evolution of these models, together with present and future observations, will bring us much nearer to understanding coronal energetics and dynamics.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Radio emission from coronal streamers

Different models of coronal streamers are used to calculate the radio brightness temperature at the wavelengths of observation of the Nançays Radioheliograph. Calculation are performed assuming the location of the streamer both on the disk and at the limb. Their comparison with observations show that a satisfactory agreement with a particular model can be found in the shape and in the relative enhacement of the streamer with respect to the quiet Sun, although the absolute values of the computed brightness temperatures are much higher than the observed ones.     

Mass flows in coronal loops

Although static loop models are often used to describe the structure of coronal loops, it is evident on both observational and theoretical grounds that mass motions play a crucial role in the physics of the corona and transition region. First we review the observations of emission-line broadening and wavelength shifts, which imply the presence of random motions and systematic downflows in coronal loops. Some discrepancies in the observations are discussed. It is argued that velocities due to gas pressure gradients are the most likely explanation for the observed flows. A number of models that have been proposed for these motions are reviewed. The implications of the various models on observations of the corona and transition region by SOHO are discussed.     

Chromospheric and coronal heating mechanisms

We review the mechanisms which have been proposed for the heating of stellar chromospheres and coronae. These consist of heating by acoustic waves, by slow and fast mhd waves, by body and surface Alfvén waves, by current or magnetic field dissipation, by microflare heating and by heating due to bulk flows and magnetic flux emergence. Some relevant observational evidence has also been discussed.     

Stationary flows in coronal loops

We present a study of stationary flows in closed solar coronal loops. The hydrodynamic differential equations of plasma flow and energy balance are integrated with algorithms which achieve high reliability. We present here results on the detailed synthesis of loop emission in specific bands and lines, taking into account also non-equilibrium ionization.     

Modeling of dynamic evolution of coronal loops

Parameters of expanding magnetic loops and arches and of mass flows generated by them in the corona have been computed in a 1D two-fluid approximation. Two possible trigger mechanisms of the coronal transients have been considered: (i) sudden increase of the background magnetic field strength, and (ii) heating and compression plasma inside these magnetic structures. We discuss the formation of shock waves and their dependence on dynamics and geometry of the magnetic structures.     

Observations of coronal structure during sunspot maximum

This paper presents some of the results that have been obtained from the Kitt Peak observations of coronal holes and the NRL observations of coronal transients during the recent years near sunspot maximum (1979–1981). On the average, low-latitude coronal holes of comparable size contained 3 times more flux near sunspot maximum than near the previous minimum. In the outer corona, transients occurred at the observed rate of at least 2 per day, and quiet conditions persisted during less than 15 % of the observed days. We describe a sample of the more than 800 events that we have observed so far, including the observation of a comet apparently colliding with the Sun.Paper presented at the IX-th Lindau Workshop The Source Region of the Solar Wind.Visiting Astronomer, KPNO.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Magnetic configuration of coronal streamers and threads

We give a short account of the most prominent structures of the intermediate corona. Then we propose an axially symmetrical model for coronal streamers, according to which charged particles move along magnetic surfaces whose sources are electrical currents situated in the vicinity of the photosphere. The simplest current configuration is a pair of coaxial, coplanar, circular, and oppositely directed currents parallel to the photosphere. Magnetic surfaces for this current distribution exhibit a helmet-shaped separatrix and a saddle point. The temperature profile along the streamer can be predicted qualitatively if one takes into account the conservation of an adiabatic invariant in the drift theory of the charged particle motion.     

Magnetic fine structures in coronal loops

The formation of magnetic fine structures and associated electric currents is considered in the context of the coronal heating problem. The penetration of field-aligned electric currents into the lower atmosphere is discussed. It is argued that currents strong enough to heat the corona can persist only for short periods of time. The formation of thin current sheets is discussed. It is argued that photospheric magnetic structures (flux tubes) play an important role in the generation of coronal currents.     

Chromospheric and coronal heating mechanisms II

We review the mechanisms which are thought to provide steady heating of chromospheres and coronae. It appears now fairly well established that nonmagnetic chromospheric regions of latetype stars are heated by shock dissipation of acoustic waves which are generated in the stellar surface convection zones. In the case of late-type giants there is additional heating by shocks from pulsational waves. For slowly rotating stars, which have weak or no magnetic fields, these two are the dominant chromospheric heating mechanisms.Except for F-stars, the chromospheric heating of rapidly rotating late-type stars is dominated by magnetic heating either through MHD wave dissipation (AC mechanisms) or through magnetic field dissipation (DC mechanisms). The MHD wave and magnetic field energy comes from fluid motions in the stellar convection zones. Waves are also generated by reconnective events at chromospheric and coronal heights. The high-frequency part of the motion spectrum leads to AC heating, the low frequency part to DC heating. The coronae are almost exclusively heated by magnetic mechanisms. It is not possible to say at the moment whether AC or DC mechanisms are dominant, although presently the DC mechanisms (e.g., nanoflares) appear to be the more important. Only a more detailed study of the formation of and the dissipation in small-scale structures can answer this question.The X-ray emission in early-type stars shows the presence of coronal structures which are very different from those in late-type stars. This emission apparently arises in the hot post-shock regions of gas blobs which are accelerated in the stellar wind by the intense radiation field of these stars.     

A self-normalizing gradient search adaptive array algorithm

A method is described to normalize the step parameter and perturbation amount used for gradient search adaptive algorithms. The step normalization assures rapid stable convergence. The perturbation normalization also assures rapid stable convergence and limits the output perturbation noise to a level below thermal noise. The normalizations are computationally simple and are consistent with the use of a single receiver at the adaptive array output. Results are presented to verify the robustness of the technique.<>     

Modeling coronal streamers and their eruption

Numerical solutions of the time-dependent MHD equations are used to generate ambient coronal streamer structures in a corona characteristic of that near solar minimum. The streamers are then disrupted by slow photospheric shear motion at the base of magnetic field lines within the closed field region, which is currently believed to be responsible for producing at least some CMEs. In contrast to several other simulations of this phenomena, the polytropic index is maintained at a value of 5/3 through the addition of coronal heating. Observations are used as a guide in determining the thermodynamic structure and plasma beta in the ambient corona. For a shear speed of 2.5 km/sec, the streamer configuration evolves slowly for about 65 hours before erupting outward with the formation of a CME. The bright CME leading edge travels outward at a speed of about 240 km/sec, and the sheared field lines follow at a somewhat slower speed. A closed magnetic field region is ejected as the magnetic field lines that were opened by the CME reconnect and reform the streamer.     

UV spectral lines from coronal transients

We investigated the UV emission expected from solar coronal transients, selecting some spectral lines which will be observed with the UVCS spectrocoronagraph onboard the SOHO spacecraft. The line intensities were calculated starting from a representative, simplified model of coronal transient. We discuss how the considered intensities depend on the physical parameters of the examined structures. This work is aimed to give a contribution in defining and preparing the future observations of coronal transients and coronal mass ejections by the UVCS/SOHO.     

3D nonlinear wave heating of coronal loops

The heating of solar coronal loops by the resonant absorption or phase-mixing of incident wave energy is investigated in the framework of 3D nonlinear magnetohydrodynamics (MHD) by means of numerical simulations.     

Observations of the solar wind from coronal holes

The solar wind emanating from coronal holes (CH) constitutes a quasi-stationary flow whose properties change only slowly with the evolution of the hole itself. Some of the properties of the wind from coronal holes depend on whether the source is a large polar coronal hole or a small near-equatorial hole. The speed of polar CH flows is usually between 700 and 800 km/s, whereas the speed from the small equatorial CH flows is generally lower and can be <400 km/s. At 1 AU, the average particle and energy fluxes from polar CH are 2.5×10⁸ cm^–2 sec^–1 and 2.0 erg cm^–2 s^–1. This particle flux is significantly less than the 4×10⁸ cm^–2 sec^–1 observed in the slow, interstream wind, but the energy fluxes are approximately the same. Both the particle and energy fluxes from small equatorial holes are somewhat smaller than the fluxes from the large polar coronal holes.Many of the properties of the wind from coronal holes can be explained, at least qualitatively, as being the result of the effect of the large flux of outward-propagating Alfvén waves observed in CH flows. The different ion species have roughly equal thermal speeds which are also close to the Alfvén speed. The velocity of heavy ions exceeds the proton velocity by the Alfvén speed, as if the heavy ions were surfing on the waves carried by the proton fluid.The elemental composition of the CH wind is less fractionated, having a smaller enhancement of elements with low first-ionization potentials than the interstream wind, the wind from coronal mass ejections, or solar energetic particles. There is also evidence of fine-structure in the ratio of the gas and magnetic pressures which maps back to a scale size of roughly 1° at the Sun, similar to some of the fine structures in coronal holes such as plumes, macrospicules, and the supergranulation.     

The coronal context of transition region explosive events

Transition region explosive events are observed throughout the quiet Sun and represent an interesting local heating phenomenon. The coronal counterparts of these events, if they exist, were not observed in a sounding rocket campaign dedicated to this objective. The coronal instrument complement on the SOHO spacecraft provides an opportunity to extend this search for the coronal counterparts of the transition region explosive events, as well as to explore the correspondence of explosive events with large scale coronal structures, such as with coronal dark lanes.     

X-Ray spectroscopic investigation of the coronal structure of capella

The binary system Capella (G6 III + F9 III) has been observed on 1979 March 15 and on 1980 March 15–17 with the Objective Grating Spectrometer (OGS) onboard theEinstein Observatory. The spectrum measured with the 1000 l/mm grating covers the range 5–30 Å with a resolution < 1 Å. The spectra show evidence for a bimodal temperature distribution of emission measure in an optically thin plasma with one component 5 million degrees and the other one 10 million degrees. Spectral features can be identified with line emissions from O VIII, Fe XVII, Fe XVIII, Fe XXIV, and Ne X ions. Good spectral fits have been obtained assuming standard cosmic abundances. The data are interpreted in terms of emission from hot static coronal loops rather similar to the magnetic arch structures found on the Sun. It is shown that the conditions required by this model exist on Capella. Mean values of loop parameters are derived for both temperature components.