MHD waves in coronal loops with a shell

We consider a model of a coronal loop in the form of a cord surrounded by a coaxial shell. Two slow magnetosonic waves longitudinally propagate within a thin flux tube on the m=0 cylindrical mode with velocities close to the tube velocities in the cord and the shell. One wave propagates inside the cord, while the other propagates inside the shell. A peculiar feature of the second wave is that the plasma in the cord and the shell oscillates with opposite phases. There are two fast magnetosonic waves on each of the cylindrical modes with m>0. If the plasma density in the shell is lower than that in the surrounding corona, then one of the waves is radiated into the corona, which causes the loop oscillations to be damped, while the other wave is trapped by the cord, but can also be radiated out under certain conditions. If the plasma density in the shell is higher than that in the cord, then one of the waves is trapped by the shell, while the other wave can also be trapped by the shell under certain conditions. In the wave trapped by the shell and the wave radiated by the tube, the plasma in the cord and the shell oscillates with opposite phases.     

Magnetic source regions of coronal mass ejections

The majority of flare activity arises in active regions which contain sunspots, while Coronal Mass Ejection (CME) activity can also originate from decaying active regions and even so-called quiet solar regions which contain a filament. Two classes of CME, namely flare-related CME events and CMEs associated with filament eruption are well reflected in the evolution of active regions. The presence of significant magnetic stresses in the source region is a necessary condition for CME. In young active regions magnetic stresses are increased mainly by twisted magnetic flux emergence and the resulting magnetic footpoint motions. In old, decayed active regions twist can be redistributed through cancellation events. All the CMEs are, nevertheless, caused by loss of equilibrium of the magnetic structure. With observational examples we show that the association of CME, flare and filament eruption depends on the characteristics of the source regions:

?the strength of the magnetic field, the amount of possible free energy storage,

?the small- and large-scale magnetic topology of the source region as well as its evolution (new flux emergence, photospheric motions, cancelling flux), and

?the mass loading of the configuration (effect of gravity). These examples are discussed in the framework of theoretical models.

     

Non-equilibrium ionization in coronal loops

The ionization conditions in coronal loops are investigated in the temperature range 2 × 10⁵–2 × 10⁶K, assuming velocity, density and temperature distributions computed for a siphon model of a pure hydrogen plasma. Use is made of the set of the carbon ions as an example of the general behaviour of the ions characteristic of that temperature range. It is found that the deviation from equilibrium ionization is large for subsonic-supersonic flow if the density is less than 5 × 10⁹cm^–-3, with the exception of the lower part of the first leg of very cool loops (T 2 × 10 K). With this exception cooler loops, given their larger density drop along the axis, show deviations from ionization equilibrium more easily than hotter ones, in spite of their lower flow velocity. We conclude that the possibility of a non-equilibrium state must be taken into account when deducing from measurements of line intensities the temperature of loops in which a flow may occur.Now at Institute for Plasma Research, Stanford University, as an E.S.A. Fellow.     

The source regions of solar coronal mass ejections

Knowledge of the origin of the solar coronal mass ejection (CME) may be crucial to our understanding of several active solar phenomena, such as flares, as well as to the structure and stability of the corona and the prediction of interplanetary disturbances. In recent years, two camps of opinion have emerged, based on the belief that CMEs either commonly originate from structures intimately linked to active regions or they originate from coronal hole regions. This present study investigates the locations of 95 CME events observed during 1984–1986 relative to coronal hole and active region features. We find no evidence to support the coronal hole hypothesis and many indications that active regions are indeed associated with the source regions of CMEs.     

Nonlinearly selected frequencies in coronal loops

A nonlinear process for the resonant generation of low-frequency fast magnetosonic kink waves in coronal loops is discussed. The efficiency of the process is strongly enhanced due to the existence of a nonlinearly selected frequency produced by a constant frequency difference in the dispersion curves in the short wavelength limit. The kink wave with the selected frequency interacts with high-frequency kink and sausage waves. The efficiency of such interaction does not require coherence in the interactive waves. In a loop of width 2 × 10³ km, field strength 50 G and number density 5 × 10¹⁵ m^–3, the nonlinearly selected frequency is of order 46 mHz (period 21.8 s), but this may range through 11 mHz to 184 mHz (periods 86.5 s to 5.4 s) for typical coronal conditions.     

Current confinement in solar coronal loops

In this paper solar coronal loops are regarded as regions of localized current flows. The main purpose is to investigate the consequences of current confinement rather than to produce a model. The physical and observational basis for this assumption are presented as well as the connection with previous studies on loop structure. A proper choice of the current profile allows us to treat quantitatively the equilibrium structure of the loops and their MHD and resistive stability properties. Regions of absolute stability against ideal kink modes are found. Explicit growth rates for the tearing-mode instability are computed. The possible relevance of other resistive effects is also discussed and the crucial importance of the small-scale geometry of the magnetic field outlined.     

Electric fields in coronal magnetic loops

We analyze spectra taken with the 40 cm coronograph at Sacramento Peak Observatory, for evidence of Stark effect on Balmer lines formed in coronal magnetic structures. Several spectra taken near the apex of a bright post-flare loop prominence show significant broadening from H₁₀ to the limit of Balmer line visibility in these spectra, at about H₂₀ The most likely interpretation of the increasing width is Stark broadening, although unresolved blends of Balmer emissions with metallic lines could also contribute to the trend. Less significant broadening is seen in 3 other post-flare loops, and the data from 5 other active coronal condensations observed in this study show no broadening tendency at all, over this range of Balmer number. The trend clearly observed in one post-flare loop requires an ion density of n _i ? 2 × 10¹² cm^?3, if it is to be explained entirely as Stark effect caused by pressure broadening. But mean electron densities measured directly from the Thomson scattering at λ3875 in the same SPO spectra, yield n _e ? 3?7 × 10¹⁰ cm^?3 for the same condensations observed within that loop. Comparison of this evidence from electron scattering, with densities derived from emission measures and line-intensity ratios, argues against a volume filling factor small enough to reconcile the values of n _i and n _e derived in this study. This discrepancy leads us to suggest that the Stark effect observed in these loops, and possibly also in flares, could be caused by macroscopic electric fields, rather than by pressure broadening. The electric field required to explain the Stark broadening in the brightest post-flare loop observed here is approximately 170 V cm^?1. We suggest an origin for such an electric field and discuss its implications for coronal plasma dynamics.     

Loss of equilibrium in coronal loops

The loss of equilibrium in coronal magnetic field structures is a possible source of energy for coronal heating and solar flares. We investigate whether such a loss of equilibrium occurs when a coronal loop is progressively twisted by photospheric motions. In studies of 2-D cylindrical equilibria, long loops have been found to be of constant cross-sectional area along most of their length, with axial variations being confined to narrow boundary layers. We use this information to develop a 1-D line-tied model, for a 2-D coronal loop. We specify the twist in terms of the azimuthal field and more physically, in terms of the photospheric footpoint displacement. In the former case we find a loss of equilibrium, but not in the latter. We also examine a twisted loop with a non-zero plasma pressure. The loss of equilibrium is only found at high-plasma . It is conjectured that such high- can occur in flare loops and prior to a prominence eruption. However, when the plasma evolves adiabatically, there is no loss of equilibrium.     

Models of dynamic coronal loops

This paper reviews the basic ideas underlying one-dimensional fluid dynamic models of coronal loops and presents some of their most recent applications. These models are an important theoretical support to explore the new scenario provided by the data of Yohkoh, SOHO, and TRACE, and are useful to interpret observations, when supplemented by appropriate spectral synthesis codes. Possible developments are also discussed.     

Plasma flow around coronal loops

Current dissipation models of coronal loop heating are studied. Turbulent current dissipation is shown to lead to a time dependent process because of an enormous mass motion induced in the current layer. A stationary heating process involves only ohmic heating, which requires a large current layer. To insure MHD stability, the loop must be composed of many elements with the oppositely directed currents. A stationary current dissipation process induces the plasma motion across the magnetic field into the loop and down the loop with the speeds v 10⁴ cm s^–1 and v 10⁴ cm s^–1, respectively. The pressure of the loop is also estimated to be proportional to the current density: p/J=6.3 × 10^-8dyn/statamp.     

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.     

The structure of coronal loops

With the advent of space telescopes, coronal magnetic loops, both within and outside active regions, are being observed with renewed interest. This paper is an attempt to outline some general physical considerations pertinent to such loops, as a prelude to more sophisticated modelling. For example, a loop that is stretched (or possibly twisted) too much may be subject to a thermal instability that cools its core to a new equilibrium below 10⁵ K. Also a simple consequence of hydrostatic balance along an equilibrium loop is that, under some circumstances, the density inside a cool loop can be comparable with that outside, despite the much smaller scale height. Finally, when the equilibrium loop density is less than the ambient density, several small scale magnetohydrodynamic instabilities are sometimes efficient enough to generate a circulation that tends to equalize the densities.     

Energy equilibrium in coronal magnetic loops -reinvestigated

Temperature distribution in cylindrically symmetric coronal magnetic loops has been reinvestigated under various conditions: (a) loop with the pressure varying along the radial distance, and (b) loop with constant pressure, for cooler apex loops and hotter apex loops. This work is reinvestigation of our previous work published inAstrophysics and Space Science (Chandra and Prasad, 1993b).     

Thermally isolated coronal loops in hydrostatic equilibrium

Numerical solutions are presented for the summit temperature and heating in a thermally isolated coronal loop that is in hydrostatic equilibrium. The extent to which gravity modifies the usual uniform-pressure scaling law is shown, and plots of the differential emission measure are also given.     

Theory of radio pulsations in coronal loops

Pulsations include a wide range of phenomena from strictly sinusoidal oscillations up to quasiperiodic fine structures, observed in the radio, microwave and X-ray frequency range. The various versions of pulsation models are reviewed and classified in three groups according to their driver mechanisms: (1) Magnetic flux tube oscillations (the emissivity of trapped particles is modulated by a standing or propagating MHD wave), (2) cyclic self-organizing systems of plasma instabilities (wave-particle, wave-wave interactions), and (3) modulation of acceleration (acceleration/injection of particles into the source). Observational references illustrate the applicability of the models. In conclusion, discrimination criteria of models are discussed, in order to give a key for interpretation of observations.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 10⁴ K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 10⁵ K, cool loops which are cooler than 8 × 10⁴ K along their whole length and hot-cool loops which have summit temperatures around 2 × 10⁴ K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 10⁴K to 4 × 10⁵ K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.     

The thermal statics of coronal loops

The thermal statics of constant pressure coronal loops is discussed, with particular emphasis on non-equilibrium and scaling relations. An analytical solution showing explicitly the occurrence of non-equilibrium in radiation dominated loops is presented. In addition, the general scaling law for hot loops is given. However, in view of the uncertainties in the coronal heating function and the observational determined loop parameters, it is suggested that scaling laws are currently of limited value.     

Radial oscillations of current-carrying coronal loops

The radial oscillations of coaxial magnetic flux tubes with an azimuthal field in the shell modeling current-carrying coronal loops are studied in the cool plasma approximation. Since the concept of current-carrying coronal loops provides a theoretical basis for studying simple loop flares, finding their parameters by means of coronal seismology is a topical problem of modern solar physics. The dispersion equation for radial oscillations is derived and the dispersion curves are constructed. Oscillations with arbitrarily long periods are shown to exist at the fundamental radial mode.     

The structure of coronal magnetic loops

We present here a model, based on observations, for the magnetic-field equilibrium of a cool coronal loop. The pressure structure, taken from the Harvard/Skylab EUV data, is used to modify the usual force-free-field form in quasi-cylindrical symmetry. The resulting field, which has the same direction but different strength, is calculated and its variation displayed. Finally, localized interchange stability is evaluated and discussed, as the first step in a subsequent complete magnetohydrodynamic-stability analysis.     

The evolution of twisted coronal loops

The evolution of coronal loops in response to slow photospheric twisting motions is investigated using a variety of methods. Firstly, by solving the time-dependent equations it is shown that the field essentially evolves through a sequence of 2-D equilibria with no evidence of rapid dynamic evolution. Secondly, a sequence of 1-D equilibria are shown to provide a remarkably good approximation to the 2-D time-dependent results using a fraction of the computer time. Thus, a substantial investigation of parameter space is now possible. Finally, simple bounds on the 3-D stability of coronal loops are obtained. Exact stability bounds can be found by using these bounds to reduce the region of parameter space requiring further investigation. Twisting the loop too much shows that a 3-D instability must be triggered.