The heating of the solar corona

In this paper a discussion is given of the present state of the theory of the heating of the solar corona by shock waves. Arguments are presented why the main contribution to the mechanical energy flux is of acoustic origin, while estimates for the amount of acoustic energy generated in the convection zone as well as the deviations from isotropy are given. During propagation through the atmosphere acoustic waves develop into shock waves after a distance of a few scale heights in the chromosphere. The heating of the outer layers by dissipation of shock waves is found to be sufficient to account for the observed radiative and corpuscular energy losses.Much emphasis is laid on the competitive role played by the four fundamental processes of energy transfer: mechanical heating, radiation, heat conduction and convection of energy in establishing the equilibrium structure of the corona. The atmosphere may be divided in several regions according to the predominance of one of the energy processes mentioned above.The physical properties of the chromosphere and the solar wind are discussed only where they are intimately connected with the problem of the heating of the corona.The most important aspects of the influence of a magnetic field on the structure and the heating of the corona in magnetically active regions are briefly mentioned. Special attention is paid to the strong channelling of heat flow along the field lines and its consequences for the structure and dynamics of the chromosphere-corona transition layer.     

Current dissipation within the chromosphere-corona transition

Studies of sporadic outbursts, ranging from flares to nano-flares, invariably endow the solar corona with steady plasma conditions, prior to seeking a current-flow (or the associated magnetic structure) which induces instability. Such an approach does not incorporate a crucial feature of the natural configuration, namely, that the material is of chromospheric origin, and only resides at coronal altitudes for as long as it can acquire adequate energy. There is clearly a feedback loop involved, which allows plasma to moderate the transfer of energy from the field while making use of this heat to permeate coronal altitudes. An examination of the whole procedure is necessary if the location and threshold-conditions for the energy-conversion mechanism are to be identified.A critical step in the feedback procedure mentioned involves the supply line which links the corona to the chromosphere. Because the solar atmosphere has such large vertical dimensions, even a modest change in average temperature and/or density can place heavy demands on this artery: the problem is that a conventional conduction-dominated transition layer cannot readily accommodate a rapid increase in current-density or plasma-flow. (Restructuring of the temperature gradient, to provide the carriers with extra heat, is a very slow process.) A transition layer of this type is unable to endure for long at the base of a sporadically-heated atmosphere in any case, since it becomes the target for plasma falling in the gravitational field during each intermediate cooling phase. As a result, the gap between the chromosphere and corona is more abrupt than is usually considered, endowing the region with thermo-electric characteristics which allow energy to be extracted when modest current-densities arise. Energy-conversion at this region fulfills two rôles: it supplies at least part of the heat required by the overlying corona, and maintains contact between the chromosphere and corona via non-thermal transport processes.     

Observations of the Sun at Vacuum-Ultraviolet Wavelengths from Space. Part II: Results and Interpretations

In Part I of this review, the concepts of solar vacuum-ultraviolet (VUV) observations were outlined together with a discussion of the space instrumentation used for the investigations. A section on spectroradiometry provided some quantitative results on the solar VUV radiation without considering any details of the solar phenomena leading to the radiation. Here, in Part II, we present solar VUV observations over the last decades and their interpretations in terms of the plasma processes and the parameters of the solar atmosphere, with emphasis on the spatial and thermal structures of the chromosphere, transition region and corona of the quiet Sun. In addition, observations of active regions, solar flares and prominences are included as well as of small-scale events. Special sections are devoted to the elemental composition of the solar atmosphere and theoretical considerations on the heating of the corona and the generation of the solar wind.     

Magneto-gravity Waves Trapped in the Lower Solar Corona

The possibility of trapped magneto-gravity waves in the lower solar corona with an open magnetic field is discussed. Intensity variations and/or Doppler shifts of relevant UV, EUV and x-ray spectral lines in the chromosphere, transition region and lower corona may reveal the existence of such low-frequency modes (with periods longer than ∼ 1.5 hour). The spectrum may be either discrete or continuous depending on the reflection property of the narrow transition region. These modes can be utilized to probe the dynamics of the upper chromosphere, transition region and lower corona; they may also play an important role in coronal heating. This revised version was published online in June 2006 with corrections to the Cover Date.     

The transition region and corona associated with sunspots

To the present time, no structure has been identified immediately above the chromosphere in sunspots that is invariably present and that thus might be called the transition region and corona over the spot. But the magnetic flux tubes emerging from spots give rise to many of the plasma filled loops that characterize the active region corona. These emit strongly from ions characteristic of the transition region, or the corona, but seldom both simultaneously. This paper presents an overview of the morphology, evolution and theory of these structures.Invited review presented at the Joint Meeting of IAU Commissions 10, 12, and 44, The MHD of Sunspots, in Montreal, 20 August 1979.     

SOHO contribution to the understanding of mass supply and flows in the solar corona

We expect a variety of dynamic phenomena in the quiescent non-flaring corona. Plasma flows, such as siphon flows or convective flows of chromospheric material evaporating into the corona, are expected whenever a pressure differences is established either between the footpoints or between the coronal and chromospheric segments of a coronal loop. Such flows can induce phenomena of spatial and temporal brightness variability of the corona. In particular, evaporation induces a net mass input into the corona and consequently coronal density enhancements. Flows are also expected in the regions where energy is released during magnetic reconnection. From the observational point of view the dynamics of the solar atmosphere has been investigated in great detail mostly in the lower transition region with the HRTS, and during flares with theSolar Maximum Mission andYohkoh. The high spectral, temporal and spatial resolution of theSOHO ultraviolet spectrometers should enable us in the near future to fill the gap providing a continuous coverage from the chromosphere to the corona, in the 10⁴–10⁶ K domain, and therefore to best study the dynamics throughout the solar atmosphere.     

Transition region line-shifts in the rebound shock spicule model

Spectral emission lines created in the solar chromosphere — corona transition region show net red-shifts. It has been proposed that this may be the result of the return of spicular material. We simulate a spicule numerically using the rebound shock model and find that the resulting hydrodynamic evolution leads to a perceived up-flow in transition region spectral lines even though the average velocity in the line forming region is directed downward. The explanation for this apparent paradox is found in the correlation between density and velocity in the waves generated by the rebound shock spicule.     

Dynamical theory of the solar wind

This paper is a review of the basic theoretical dynamical properties of an atmosphere with an extended temperature strongly bound by gravity. The review begins with the historical developments leading up to the realization that the only dynamical equilibrium of an atmosphere with extended temperature is supersonic expansion. It is shown that sufficient conditions for supersonic expansion are T(r) declining asymptotically less rapidly than 1/r, or the density at the base of the corona being less than N _b given by (40) if no energy is available except through thermal conductivity, or the temperature falling within the limits given by (18) if T N ^-1 throughout the corona. Less extended temperatures lead to equilibria which are subsonic or static. The hypothetical case of a corona with no energy supply other than thermal conduction from its base is considered at some length because the equations may be solved by analytical methods and illustrate the transition from subsonic to supersonic equilibrium as the temperature becomes more extended. Comparison with the actual corona shows that the solar corona is actively heated for some distance into space by wave dissipation.The dynamical stability of the expanding atmosphere is demonstrated, and in a later section the radial propagation of acoustic and Alfvén waves through the atmosphere and wind is worked out. The calculations show that the magnetometer will probably detect waves more easily than the plasma instrument, but that both are needed to determine the mode and direction of the wave. An observer in the wind at the orbit of Earth can listen to disturbances generated in the corona near the sun and in turbulent regions in interplanetary space.The possibility that the solar corona is composed of small-scale filaments near the sun is considered. It is shown that such filamentary structure would not be seen at the orbit of Earth. It is pointed out that the expansion of a non-filamentary corona seems to lead to too high a calculated wind density at the orbit of Earth to agree with the present observations, unless T(r) is constant or increases with r. A filamentary corona, on the other hand, would give the observed wind density for declining T(r).It is shown that viscosity plays no important role in the expansion of an atmosphere either with or without a weak magnetic field. The termination of the solar wind, presumably between 10–10³ AU, is discussed briefly. The interesting development here is the interplanetary L recently observed, which may come from the interstellar neutral hydrogen drifting into the outer regions of the solar wind.Theory is at the present time concerned with the general dynamical principles which pertain to the expansion equilibrium of an atmosphere. It is to be expected that the rapid progress of direct observations of the corona and wind will soon permit more detailed studies to be carried out. It is important that the distinction between detailed empirical models and models intended to illustrate general principles be kept clearly in mind at all times.This work was supported by the National Aeronautics and Space Administration under Grant NASA-NsG-96-60.     

High-resolution ultraviolet solar observations from sounding rockets and spacelab

High spatial (1) and temporal (20 s) resolution UV spectroscopy of the Sun has been carried out with a new instrument flown on sounding rockets. These observations reveal a multitude of new highly energetic phenomena in the outer solar atmosphere which may play a decisive rôle in the mechanical energy balance of the chromosphere, transition zone and corona.Proceedings of the Conference Solar Physics from Space, held at the Swiss Federal Institute of Technology Zurich (ETHZ), 11–14 November 1980.     

Working group 1: Small scale features

A review is given of the activities of the working group on small scale features at the 2nd SOHO Workshop on Elba, 27 September–1 October 1993. The small scale and filamentary structure of the solar transition region, and possibly also the corona, was pointed out. The reported observations furthermore demonstrated that the upper solar atmosphere is strongly dynamical, containing rapidly flowing gas and with features changing with time. Theoretical concepts and simulations of conditions in the transition region and corona were presented and discussed. Finally some ideas on future observations and modelling were put forward.     

Observations of the profiles of solar UV emission lines and their analysis in terms of the heating and production of the corona

Observations of the solar spectrum have been made between 1200–2200 with high spectral resolution. The results were obtained with an all-reflecting echelle spectrograph carried by a stabilized Skylark rocket launched in April 1970. Measurements of the profiles of a number of emission lines due to Siii, Cii, Siiii and Civ formed in the temperature range 10⁴-10⁵ K, indicate ion energies which are considerably in excess of the electron temperatures derived from the ionization balance. Since the ion/electron relaxation time is very short the observed ion energies cannot correspond to an ion temperature and hence a non-thermal mechanical energy component exists in the transition zone.It is postulated that the non-thermal energy component represents the actual mechanical energy responsible for the heating of the corona, and, that, it is propagated as an acoustic wave. On this basis and with a preliminary estimate of the reflection from the transition zone, a flux of 3 × 10⁵ erg cm ^-2 s ^-1 is established as entering the corona. This value is in agreement with estimates of the total energy loss from the corona due to conduction, radiation and the solar wind, thus establishing a gross energy balance.Theoretical calculations are currently underway to establish the physical nature of the atmosphere which would result from such a propagating flux. At the present time this has been carried out for an atmosphere in hydrostatic equilibrium and the energy balance equation solved. A preliminary temperature structure which results is shown in Figure 1, together with the derived distribution in electron density. This gives a corona of the right temperature and density but the observed structure deviates in detail from those derived from an analysis of the solar XUV spectrum.     

Coupling from the Photosphere to the Chromosphere and the Corona

The atmosphere of the Sun is characterized by a complex interplay of competing physical processes: convection, radiation, conduction, and magnetic fields. The most obvious imprint of the solar convection and its overshooting in the low atmosphere is the granulation pattern. Beside this dominating scale there is a more or less smooth distribution of spatial scales, both towards smaller and larger scales, making the Sun essentially a multi-scale object. Convection and overshooting give the photosphere its face but also act as drivers for the layers above, namely the chromosphere and corona. The magnetic field configuration effectively couples the atmospheric layers on a multitude of spatial scales, for instance in the form of loops that are anchored in the convection zone and continue through the atmosphere up into the chromosphere and corona. The magnetic field is also an important structuring agent for the small, granulation-size scales, although (hydrodynamic) shock waves also play an important role—especially in the internetwork atmosphere where mostly weak fields prevail. Based on recent results from observations and numerical simulations, we attempt to present a comprehensive picture of the atmosphere of the quiet Sun as a highly intermittent and dynamic system.     

Alfvén wave heating

This review discusses Alfvén wave heating in non-uniform plasmas as a possible means for explaining the heating of the solar corona. It focusses on recent analytical results that enable us to understand the basic physics of Alfvén wave heating and help us with the interpretation of results of numerical simulations. First we consider the singular wave solutions that are found in linear ideal MHD at the resonant magnetic surface where the frequency of the wave equals the local Alfvén frequency. Next, we use linear resistive MHD for describing the waves in the dissipative region and explain how dissipation modifies the singular solutions found in linear ideal MHD.     

The Dynamic Quasiperpendicular Shock: Cluster Discoveries

The physics of collisionless shocks is a very broad topic which has been studied for more than five decades. However, there are a number of important issues which remain unresolved. The energy repartition amongst particle populations in quasiperpendicular shocks is a multi-scale process related to the spatial and temporal structure of the electromagnetic fields within the shock layer. The most important processes take place in the close vicinity of the major magnetic transition or ramp region. The distribution of electromagnetic fields in this region determines the characteristics of ion reflection and thus defines the conditions for ion heating and energy dissipation for supercritical shocks and also the region where an important part of electron heating takes place. In other words, the ramp region determines the main characteristics of energy repartition. All these processes are crucially dependent upon the characteristic spatial scales of the ramp and foot region provided that the shock is stationary. The process of shock formation consists of the steepening of a large amplitude nonlinear wave. At some point in its evolution the steepening is arrested by processes occurring within the shock transition. From the earliest studies of collisionless shocks these processes were identified as nonlinearity, dissipation, and dispersion. Their relative role determines the scales of electric and magnetic fields, and so control the characteristics of processes such as ion reflection, electron heating and particle acceleration. The determination of the scales of the electric and magnetic field is one of the key issues in the physics of collisionless shocks. Moreover, it is well known that under certain conditions shocks manifest a nonstationary dynamic behaviour called reformation. It was suggested that the transition from stationary to nonstationary quasiperiodic dynamics is related to gradients, e.g. scales of the ramp region and its associated whistler waves that form a precursor wave train. This implies that the ramp region should be considered as the source of these waves. All these questions have been studied making use observations from the Cluster satellites. The Cluster project continues to provide a unique viewpoint from which to study the scales of shocks. During its lifetime the inter-satellite distance between the Cluster satellites has varied from 100 km to 10000 km allowing scientists to use the data best adapted for the given scientific objective. The purpose of this review is to address a subset of unresolved problems in collisionless shock physics from experimental point of view making use multi-point observations onboard Cluster satellites. The problems we address are determination of scales of fields and of a scale of electron heating, identification of energy source of precursor wave train, an estimate of the role of anomalous resistivity in energy dissipation process by means of measuring short scale wave fields, and direct observation of reformation process during one single shock front crossing.     

Driving mechanisms for the solar wind

In this review, we consider the central physical aspects pertinent to the acceleration of the solar wind. Special importance is placed on the high-speed streams since the properties of these structures seem to strain the various theoretical explanations the most. Heavy emphasis is also given to the observations — particularly as to what constraints they place on the theories. We also discuss certain sporadic events such as spicules, macrospicules, X-ray bright points, and outflows seen in the EUV associated with the explosive events, jets, and coronal bullets which could be of relevance to this problem.Three theoretical concepts pertaining to the solar wind acceleration process are examined — purely thermal acceleration with and without extended heating, acceleration due to Alfvén wave pressure, and diamagnetic acceleration. Emphasis is given to how well these theories meet the constraints imposed by the observations. Diamagnetism is argued to be a powerful ingredient in solar wind theory, both in the light of observed sporatic outflows seen in the chromosphere and transition region and also because of its effectiveness in increasing the flow speed and producing strong acceleration near the Sun in line with coronal hole observations.     

Identifications of emission lines in the EUV solar spectrum

Conclusions During the past three years there have been significant extensions of the solar data available. Over most of the solar spectrum between 1 – 2200 the new or improved observations have led to interesting problems in line identifications. The identifications have in turn led to new methods of determining the physical conditions in the solar atmosphere, eg electron density determinations from the Hei like ion intercombination line to forbidden line ratio (Gabriel and Jordan, 1969b). The majority of the strong lines have now been identified, either by theoretical considerations or from the extensive laboratory data which have recently become available. However, weak lines may also aid the understanding of the chromosphere and corona and work on the identifications of all remaining features observed must continue.     

Observational Aspects of Particle Acceleration in Large Solar Flares

Solar flares efficiently accelerate electrons to several tens of MeV and ions to 10 GeV. The acceleration is usually thought to be associated with magnetic reconnection occurring high in the corona, though a shock produced by the Coronal Mass Ejection (CME) associated with a flare can also accelerate particles. Diagnostic information comes from emission at the acceleration site, direct observations of Solar Energetic Particles (SEPs), and emission at radio wavelengths by escaping particles, but mostly from emission from the chromosphere produced when the energetic particles bombard the footpoints magnetically connected to the acceleration region. This paper provides a review of observations that bear upon the acceleration mechanism.     

The Morphology of the Solar Upper Atmosphere During the Sunspot Minimum

The solar upper atmosphere (SUA) is defined as the volume above the photosphere occupied by plasmas with electron temperatures, T _e, above 2×10⁴ K. Until the Skylab era, only little was known about the morphology of the SUA, while the quality of the spectroscopic observations was continually improving. A spherically symmetric atmosphere was assumed at that time, in which the temperature increased with height. With advances in the observational techniques, it became apparent that the morphology of the SUA was very complex even during the minimum of the magnetic activity cycle. In particular, spectroscopic measurements with high spectral and spatial resolution, which were made in the light of ultraviolet emission lines representing a variety of temperatures, led to the conclusion that most of the radiation from the solar transition region could not be explained by assuming a continuous chromosphere-corona interface, but rather by a region of unresolved fine structures. Recent observational results obtained by modern instruments, such as the Extreme-ultraviolet Imaging Telescope (EIT), the Large Angle Spectroscopic Coronagraph (LASCO), and the Solar Ultraviolet Measurements of (SUMER) spectrograph on the Solar and Heliospheric Observatory (SOHO), as well as the Transition Region and Coronal Explorer (TRACE), and their interpretations will be presented in this review of our understanding of the morphology of the SUA.     

Solar Fine-Scale Structures. I. Spicules and Other Small-Scale, Jet-Like Events at the Chromospheric Level: Observations and Physical Parameters

Over the last two decades the uninterrupted, high resolution observations of the Sun, from the excellent range of telescopes aboard many spacecraft complemented with observations from sophisticated ground-based telescopes have opened up a new world producing significantly more complete information on the physical conditions of the solar atmosphere than before. The interface between the lower solar atmosphere where energy is generated by subsurface convection and the corona comprises the chromosphere, which is dominated by jet-like, dynamic structures, called mottles when found in quiet regions, fibrils when found in active regions and spicules when observed at the solar limb. Recently, space observations with Hinode have led to the suggestion that there should exist two different types of spicules called Type?I and Type?II which have different properties. Ground-based observations in the Ca?ii H and K filtergrams reveal the existence of long, thin emission features called straws in observations close to the limb, and a class of short-lived events called rapid blue-shifted excursions characterized by large Doppler shifts that appear only in the blue wing of the Ca?ii infrared line. It has been suggested that the key to understanding how the solar plasma is accelerated and heated may well be found in the studies of these jet-like, dynamic events. However, while these structures are observed and studied for more than 130 years in the visible, but also in the UV and EUV emission lines and continua, there are still many questions to be answered. Thus, despite their importance and a multitude of observations performed and theoretical models proposed, questions regarding their origin, how they are formed, their physical parameters, their association with the underlying photospheric magnetic field, how they appear in the different spectral lines, and the interrelationship between structures observed in quiet and active regions on the disk and at the limb, as well as their role in global processes has not yet received definitive answers. In addition, how they affect the coronal heating and solar wind need to be further explored. In this review we present observations and physical properties of small-scale jet-like chromospheric events observed in active and quiet regions, on the disk and at the limb and discuss their interrelationship.