Siphon flows in coronal loops: I. Adiabatic flow

It is now known that the corona is filled with a multitude of loop-like structures. The likelihood of these loops being in static equilibrium is small and so this paper explores the possibility of steady isothermal or adiabatic flows, driven by a pressure difference between the loop feet. For a symmetric loop the flow becomes supersonic at the summit and is then retarded by a shock-wave at some point on the downflowing leg. The effect of adiabatic flow is to lower both pressure and temperature by at least a factor of two and so provide a possible explanation for the cool cores that are sometimes observed in coronal loops. Asymmetric loops, whose cross-sectional area increases or decreases in the flow direction, are found to possess a wide range of both subsonic and shocked flows. Converging loops have subsonic flows if the pressure difference between the footpoints is small, but shocked flows if the pressure difference is large enough. Diverging loops exhibit only shocked flows towards a low pressure footpoint, but can have either subsonic or shocked flow towards a high pressure footpoint. Flows in diverging loops can therefore be either accelerated or decelerated.     

Ray-type spectra of plasma turbulence in coronal magnetic loops

The problem of stationary spectra of Langmuir, l, and electromagnetic, t, waves excited in a magnetic trap (loop) by a group of suprathermal electrons, whose velocity distribution includes a loss cone, is considered. Within the framework of weak turbulence theory, accurate spectra of l- and t-waves are found. These spectra have the form of thin rays in wavevector space. Forms of plasma emission radio lines of a homogeneous source near the plasma frequency and its second harmonic are determined.     

X-ray observations of limb flare loops and post-flare coronal arch

We present observations of another post-flare arch following an eruptive flare, detected in X-ray lines above the western solar limb on 2 May 1985.     

Structure of coronal holes from UV and radio observations

The coronal hole observed on May 31, 1973 is studied using extreme ultraviolet and radio observations. The EUV line is the Fe xv at = 284 Å and the radio frequencies are 169 and 408 MHz. An unsuccessful attempt to deduce an homogeneous model of the hole from these observations, shows that EUV and radio observations are inconsistent if interpreted in such a frame and if the EUV line intensity measurements in the hole are reliable.Inhomogeneities are therefore required to account for both observations. An inhomogeneous model consisting of hot (T2×10⁶K) elements covering 10% of the hole surface surrounded by regions of colder gas (T8×10⁵K) is able to explain both observations.     

Flares and plasma flow caused by interacting coronal loops

Active region NOAA 7360 was observed in 1992 December with various instruments including the Yohkoh satellite. In this region, a small loop emerged near one of the footpoints of a pre-existing large coronal loop. These loops show evidence that interactions between coronal loops cause flares, microflares, and plasma flow. All of the four flares observed in this region show that brightenings in the small loop occurred first, and then the large loop flared up. The brightenings in the large loop can not occur by themselves, but must be triggered by the brightenings in the small loop. There must be interactions between the loops to cause these flares. As well as the flares, many microflares occurred in the small loop. More than half of them are accompanied by plasma ejection phenomena from the small loop into the large loop. The large loop is filled with ejected plasma with velocities of about 1000 km s^–1. These ejection phenomena are considered as X-ray jets. The associated occurrences of the microflares and the jets suggest that they are also caused by interactions between the loops. The recurrent occurrences of the homologous flares and microflares mean that the magnetic field structure in this region inevitably causes the activity due to loop-loop interactions; the flares and jets occur under a common magnetic field structure.     

Inferences of plasma parameters from coronal hole observations

The temperature in the acceleration region of the solar wind remains one of the most elusive parameters to measure. Knowledge of the temperature as well as its gradient in the inner corona is fundamental for placing constraints on physical mechanisms thought to be responsible for the coronal heating process, as well as for understanding the flow properties of the solar wind. Estimates of the helium abundance is essential for understanding the puzzling behavior of heavier ions in the solar wind. As an illustration of the difficulties and uncertainties involved in the inferences of plasma parameters in the wolar wind acceleration region, The inference of electron temperature and helium abundance will be described. Prospects for future observations will be briefly discussed.     

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.     

A blowout surge from the eruption of a miniature filament confined by large coronal loops

By means of Hα, EUV, soft X-ray, hard X-ray, and photospheric magnetic field observations, we report the surge-like eruption of a small-scale filament, called “blowout surge” according to recent observations, occurring on a plage region around AR 10876 on 1 May 2006. Along magnetic polarity reversal boundaries with obvious magnetic cancelations, the filament was located underneath a compact coronal arcade and close to one end of large coronal loops around the AR’s periphery. The filament started to erupt about 8 min before the main impulsive phase of a small two-ribbon flare, which had two Hα blue-wing kernels connected by hard X-ray loop-top sources on the both sides of the filament. After the flare end, the filament further underwent a distant eruption following a path nearly along the preexisting large loops, and thus looked like an Hα surge and an EUV jet. During the eruption, a small coronal dimming was formed near the flare, while weak brightenings appeared around the remote end of the large loops. We interpret these joint observations as the filament eruption being confined and guided by the large loops. The filament eruption, initially embedded in one footpoint region of the large loops, can break away from the magnetic restraint of the overlying compact arcade, but might be still limited inside the large loops. As a result, the eruption took a surge form that can only expand laterally along the large loops rather than erupt radially.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Kink oscillations of asymmetric coronal loops

The free oscillations of coronal loops with a constant density and a variable magnetic field changing according to parabolic laws are investigated. Using our developed method, we derive the wave equations with constant coefficients that describe the kink oscillations of symmetric and asymmetric magnetic flux tubes. For such models, we obtain analytical expressions for the oscillation spectra and amplitudes as well as the magnitudes and directions of the displacements of the extrema of the fundamental and first modes relative to their values for homogeneous tubes. For the first mode of an asymmetric loop, we have determined the dependence of the coordinate displacement for the internal node on the ratios of the magnetic field strengths in its asymmetric parts and the ratio of the amplitudes at the extremum points.