Transverse Oscillations of Coronal Loops

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.     

Equivalent Electric Circuit Models of Coronal Magnetic Loops and Related Oscillatory Phenomena on the Sun

Coronal loops, which trace closed magnetic field lines, are the primary structural elements of the solar atmosphere. Complex dynamics of solar coronal magnetic loops, together with action of possible subphotospheric dynamo mechanisms, turn the majority of the coronal loops into current-carrying structures. In that connection none of the loops can be considered as isolated from the surroundings. The current-carrying loops moving relative to each other interact via the magnetic field and currents. One of the ways to take into account this interaction consists in application of the equivalent electric circuit models of coronal loops. According to these models, each loop is considered as an equivalent electric LCR-circuit with variable inductive coefficients L, capacitance C, and resistance R, which depend on shape, scale, position of the loop with respect to neighbouring loops, as well as on the plasma parameters in the magnetic tube. Such an approach enables to describe the process of electric current dynamics in the groups of coronal loops, as well as the related dynamical, energy release and radiation processes. In the present paper we describe the major principles of LCR-circuit models of coronal magnetic loops, and show their application for interpretation of the observed oscillatory phenomena in the loops and in the related radiation.     

The Evolving Sigmoid: Evidence for Magnetic Flux Ropes in the Corona Before, During, and After CMES

It is generally accepted that the energy that drives coronal mass ejections (CMEs) is magnetic in origin. Sheared and twisted coronal fields can store free magnetic energy which ultimately is released in the CME. We explore the possibility of the specific magnetic configuration of a magnetic flux rope of field lines that twist about an axial field line. The flux rope model predicts coronal observables, including heating along forward or inverse S-shaped, or sigmoid, topological surfaces. Therefore, studying the observed evolution of such sigmoids prior to, during, and after the CME gives us crucial insight into the physics of coronal storage and release of magnetic energy. In particular, we consider (1) soft-X-ray sigmoids, both transient and persistent; (2) The formation of a current sheet and cusp-shaped post-flare loops below the CME; (3) Reappearance of sigmoids after CMEs; (4) Partially erupting filaments; (5) Magnetic cloud observations of filament material.     

Progress, Challenges, and Perspectives of the 3D MHD Numerical Modeling of Oscillations in the Solar Corona

Recent high temporal and spatial resolution satellite observations of the solar corona provide ample evidence of oscillations in coronal structures. The observed waves and oscillations can be used as a diagnostic tool of the poorly known coronal parameters, such as magnetic field, density, and temperature. The emerging field of coronal seismology relies on the interpretation of the various coronal oscillations in terms of theoretically known wave modes, and the comparison of observed and theoretical wave mode properties for the determination of the coronal parameters. However, due to complexity of coronal structures the various modes are coupled, and the application of linear theory of idealized structures to coronal loops and active regions limits the usefulness of such methods. Improved coronal seismology can be achieved by the development of full 3D MHD dynamical model of relevant coronal structures and the oscillation phenomena. In addition to improved accuracy compared to linear analysis, 3D MHD models allow the diagnostic method to include nonlinearity, compressibility, and dissipation. The current progress made with 3D MHD models of waves in the corona is reviewed, and the challenges facing further development of this method are discussed in the perspective of future improvement that will be driven by new high resolution and high cadence satellite data, such as received from Hinode and STEREO, and expected from SDO.     

Dynamics of Coronal Loop Oscillations Recent Improvements and Computational Aspects

We will discuss the observed, heavily damped transversal oscillations of coronal loops. These oscillations are often modeled as transversal kink oscillations in a cylinder. Several features are added to the classical cylindrical model. In our models we include loop curvature, longitudinal density stratification, and highly inhomogeneous radial density profiles. In this paper, we will first give an overview of recently obtained results, both analytically and numerically. After that, we shed a light on the computational aspects of the modeling process. In particular, we will focus on the parallellization of the numerical codes.     

Standing Slow-Mode Waves in Hot Coronal Loops: Observations, Modeling, and Coronal Seismology

Strongly damped Doppler shift oscillations are observed frequently associated with flarelike events in hot coronal loops. In this paper, a review of the observed properties and the theoretical modeling is presented. Statistical measurements of physical parameters (period, decay time, and amplitude) have been obtained based on a large number of events observed by SOHO/SUMER and Yohkoh/BCS. Several pieces of evidence are found to support their interpretation in terms of the fundamental standing longitudinal slow mode. The high excitation rate of these oscillations in small- or micro-flares suggest that the slow mode waves are a natural response of the coronal plasma to impulsive heating in closed magnetic structure. The strong damping and the rapid excitation of the observed waves are two major aspects of the waves that are poorly understood, and are the main subject of theoretical modelling. The slow waves are found mainly damped by thermal conduction and viscosity in hot coronal loops. The mode coupling seems to play an important role in rapid excitation of the standing slow mode. Several seismology applications such as determination of the magnetic field, temperature, and density in coronal loops are demonstrated. Further, some open issues are discussed.     

Observations of loops and prominences

We review recent observations by the Yohkoh-SXT in collaboration with other spacecraft and ground-based observatories of coronal loops and prominences. These new results point to problems that SoHO will be able to address. With a unique combination of rapid-cadence digital imaging (32 s full-disk and 2 s partial-frame images), high spatial resolution (2.5 arcsec pixels), high sensitivity (EM 10⁴² cm^–3), a low-scatter mirror, and large dynamic range, SXT can observe a vast range of targets on the Sun. Over the first 21 months of Yohkoh operations, SXT has taken over one million images of the corona and so is building up an invaluable long-term database on the large-scale corona and loop geometry. The most striking thing about the SXT images is the range of loop sizes and shapes. The active regions are a bright tangle of magnetic field lines, surrounded by a network of large-scale quiet-Sun loops stretching over distances in excess of 10⁵ km. The cross-section of most loops seems to be constant. Loops displaying significant increase in the ratio of the footpoint to loop-top diameter () are the exception, not the rule, implying the presence of widespread currents in the corona.All magnetic structures show changes. Time scales range from seconds to months. The question of how these structures are formed, become filled with hot plasma, and are maintained is still open. While we see the propagation of brightenings along the length of active-region loops and in X-ray jets with velocities of several hundred km/s, much higher velocities are seen in the quiet Sun. In XBP flares, for example, velocities of over 1000 km/s are common. Active-region loops seem to be in constant motion, moving slowly outward, carrying plasma with them. During flares, loops often produce localized brightenings at the base and later at the apex of the loop. Quiescent filaments and prominences have been observed regularly. Their coronal manifestation seems to be an extended arcade of loops overlying the filament. Reliable alignment of the ground-based data with the X-ray images make it possible to make a detailed intercomparison of the hot and cold plasma structures over extended periods. Hence we are able to follow the long-term evolution of these structures and see how they become destabilized and erupt.     

Varieties of Coronal Mass Ejections and Their Relation to Flares

Most coronal mass ejections (CMEs) start as coronal storms which are caused by an opening of channels of closed field lines along the zero line of the longitudinal magnetic field. This can happen along any zero line on the Sun where the configuration is destabilized. If the opening includes a zero line inside an active region, one observes a chromospheric flare. If this does not happen, no flare is associated with the CME in the chromosphere, but the process, as well as the response in the corona (a Long Decay Event in X-rays) remains the same. The only difference between flare-associated and non-flare-associated CMEs is the strength of the magnetic field in the region of the field line opening. This can explain essentially all differences which have been observed between these two kinds of CMEs. However, there are obviously also other sources of CMEs, different from coronal storms: sprays (giving rise to narrow, pointed ejections), erupting interconnecting loops (often destabilized by flares), and growing coronal holes. This paper tries to summarize and interpret observations which support this general picture, and demonstrates that both CMEs and flares must be properly discussed in any study of solar-terrestrial relations.     

Thermal cyclotron radiation from a hot coronal loop with helical magnetic field

The spectral and polarization properties of thermal cyclotron radio emission from a hot coronal loop with a current along the axis are computed. The magnetic field is supposed to have a component along the loop axis as well as a poloidal part due to the current, both components being of comparable magnitude. In this specific configuration a helical magnetic field is present with a remarkable minimum of its absolute value along the loop axis and a maximum at its periphery. The presence of one or two maxima of magnetic field value along the line of sight results in increasing optical thickness of the gyroresonance layers at appropriate frequencies in the microwave band and, therefore, in enhanced radio emission at those harmonics which are optically thin (for example,s=4). These cannot be observed in models with the commonly employed magnetic field configuration (longitudinal along the loop axis).We show that the frequency spectrum of thermal cyclotron radiation from a hot coronal loop with a helical magnetic field differs from that of the standards-component source (with smooth frequency characteristics and polarization corresponding toe-mode) in that plenty of fine structures (line-like features and cut-offs) are present and theo-mode is prevalent in some frequency intervals. The enhanced radio emission at high harmonics and the complicated form of frequency spectrum in the model considered imply that some microwave sources, which are poorly explained in traditional models of solar active regions, may be associated with helical magnetic fields in hot coronal loops. Computations allow one to indicate spectral and polarizational peculiarities of local sources testifying to the presence of a helical magnetic field.     

In-Situ Solar Wind and Magnetic Field Signatures of Interplanetary Coronal Mass Ejections

The heliospheric counterparts of coronal mass ejections (CMEs) at the Sun, interplanetary coronal mass ejections (ICMEs), can be identified in situ based on a number of magnetic field, plasma, compositional and energetic particle signatures as well as combinations thereof. We summarize these signatures and their implications for understanding the nature of these structures and the physical properties of coronal mass ejections. We conclude that our understanding of ICMEs is far from complete and formulate several challenges that, if addressed, would substantially improve our knowledge of the relationship between CMEs at the Sun and in the heliosphere.     

Wind in the Solar Corona: Dynamics and Composition

The dynamics of the solar corona as observed during solar minimum with the Ultraviolet Coronagraph Spectrometer, UVCS, on SOHO is discussed. The large quiescent coronal streamers existing during this phase of the solar cycle are very likely composed by sub-streamers, formed by closed loops and separated by open field lines that are channelling a slow plasma that flows close to the heliospheric current sheet. The polar coronal holes, with magnetic topology significantly varying from their core to their edges, emit fast wind in their central region and slow wind close to the streamer boundary. The transition from fast to slow wind then appears to be gradual in the corona, in contrast with the sharp transition between the two wind regimes observed in the heliosphere. It is suggested that speed, abundance and kinetic energy of the wind are modulated by the topology of the coronal magnetic field. Energy deposition occurs both in the slow and fast wind but its effect on the kinetic temperature and expansion rate is different for the slow and fast wind.     

Coronal loops and prominences as observed with RATAN-600

This paper presents a short summary of observations of coronal structures at microwaves using an instrument with high spatial resolution and good wavelength coverage. The comparison of the RATAN-600 data with optical observations of coronal loops in the green line and with the Very Large Array maps at 21 cm has shown that the loops represent only a small part of coronal matter, although their role may be of great importance in the physics of the solar corona. Prominence (filament) associated sources, especially peculiar ones, are also reviewed.     

The high latitude heliospheric magnetic field

As the Ulysses spacecraft approaches its first pass under the south pole of the sun, it is an appropriate time to review our current knowledge and predictions regarding the three dimensional behaviour of the heliospheric magnetic field, in particular at high heliographic latitudes. Optical techniques for measuring the photospheric magnetic field and observations of coronal brightness structures provide indications of the behaviour of the source of the heliospheric field in the corona. As the coronal fields are carried out into the heliosphere by the solar wind, from Parker's model we would expect that the spiral field observed in the equatorial plane should gradually unwind with latitude leading to open, approximately radial, field lines over the polar regions. Predictions of departures from, and models extending this simple picture are discussed. Both the Pioneer and Voyager spacecraft have spent brief periods in the regions above the maximum latitude of the heliospheric current sheet-relevant results from these missions are reviewed as well as results from the early stages of the out-of-ecliptic phase of the Ulysses mission. The configuration of the coronal magnetic field exhibits a strong dependence on the phase of the solar activity cycle. While the forthcoming Ulysses polar passes take place near to solar minimum, the different conditions which might be encountered on a second orbit of the sun at solar maximum are described.     

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.     

Structure and development of quiet loops in the solar corona

X-ray emission from solar coronal loops changes on two different timescales: a) flare loops and transient active region brightenings show a rapid variability, b) quiet region loops are quasi-steady and change only slowly with time. This different time behavior has been analyzed on the basis of Yohkoh SXT observations and we report here on the results from our analysis, mainly focussing on quiet loop variability.     

MHD Waves and Instabilities in Space Plasma Flows

Shear flow instabilities are an important aspect of hydrodynamic studies. The present review article discusses the role of an ambient magnetic field which both modifies the Kelvin-Helmholtz instability and may introduce new types of magnetohydrodynamic waves and instabilities. A brief overview of magnetospheric pulsations is presented with an emphasis on the long-period resonant Alfv??n waves associated with the high speed solar wind. The spatio-temporal evolution of magnetically modified shear flow instabilities in various space plasma structures is addressed. A distinction between convective and absolute instabilities is necessary for proper understanding of theory and correct interpretation of the observations. Finally, it is shown how incompressible Alfv??nic disturbances may become unstable in a compressible flow in the absence of any shear. An application to coronal loops is presented.     

Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 3. Physical Implications

We conclude the heliospheric image series with this third and final instalment, where we consider the physical implications of our reconstruction of interplanetary coronal mass ejections from heliospheric imagers. In Paper 1 a review of the theoretical framework for the appearance of ICMEs in the heliosphere was presented and in Paper 2 a model was developed that extracted the three-dimensional structure and kinematics of interplanetary coronal mass ejections directly from SMEI images. Here we extend the model to include STEREO Heliospheric Imager data and reproduce the three-dimensional structure and kinematic evolution of a single Earth-directed interplanetary coronal mass ejection that was observed in November 2007. These measurements were made with each spacecraft independently using leading edge measurements obtained from each instrument. We found that when data from the three instruments was treated as a single collective, we were able to reproduce an estimate of the ICME structure and trajectory. There were some disparities between the modelled ICME and the in situ data, and we interpret this as a combination of a slightly more than spherically curved ICME structure and a corotating interaction region brought about by the creation of a coronal hole from the CME eruption. This is the first time evidence for such a structure has been presented and we believe that it is likely that many ICMEs are of this nature.     

The Solar Origin of Corotating Interaction Regions and Their Formation in the Inner Heliosphere

Corotating Interaction Regions (CIRs) form as a consequence of the compression of the solar wind at the interface between fast speed streams and slow streams. Dynamic interaction of solar wind streams is a general feature of the heliospheric medium; when the sources of the solar wind streams are relatively stable, the interaction regions form a pattern which corotates with the Sun. The regions of origin of the high speed solar wind streams have been clearly identified as the coronal holes with their open magnetic field structures. The origin of the slow speed solar wind is less clear; slow streams may well originate from a range of coronal configurations adjacent to, or above magnetically closed structures. This article addresses the coronal origin of the stable pattern of solar wind streams which leads to the formation of CIRs. In particular, coronal models based on photospheric measurements are reviewed; we also examine the observations of kinematic and compositional solar wind features at 1 AU, their appearance in the stream interfaces (SIs) of CIRs, and their relationship to the structure of the solar surface and the inner corona; finally we summarise the Helios observations in the inner heliosphere of CIRs and their precursors to give a link between the optical observations on their solar origin and the in-situ plasma observations at 1 AU after their formation. The most important question that remains to be answered concerning the solar origin of CIRs is related to the origin and morphology of the slow solar wind. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electrodynamics of the outer solar atmosphere

The structure of the outer solar atmosphere and its magnetic coupling to the photospheric motions indicate the existence of large-scale current systems. The heating and the dynamics of coronal structures is therefore governed by electrodynamic coupling of these structures to the underlying photosphere. In a structured corona, the heating is enhanced because of several processes such as resonance absorption of Alfvénic surface waves, anomalous Joule heating, reconnection and the related topological dissipation. The global thermal and dynamic behaviour of coronal structures can be fruitfully described in terms of equivalent electrodynamic circuits, taking into account the paramount role of the photospheric boundaries. Coronal current systems may be stable, as in the case of coronal loops, but occassionally they show catastrophic behaviour if the current intensity surpasses a critical threshold.     

Coronal plumes and fine scale structure in high speed solar wind streams

We present a solar wind model which takes into account the possible origin of fast solar wind streams in coronal plumes. We treat coronal holes as being made up of essentially 2 plasma species, denser, warmer coronal plumes embedded in a surrounding less dense and cooler medium. Pressure balance at the coronal base implies a smaller magnetic field within coronal plumes than without. Considering the total coronal hole areal expansion as given, we calculate the relative expansion of plumes and the ambient medium subject to transverse pressure balance as the wind accelerates. The magnetic flux is assumed to be conserved independently both within plumes and the surrounding coronal hole. Magnetic field curvature terms are neglected so the model is essentially one dimensional along the coronal plumes, which are treated as thin flux-tubes. We compare the results from this model with white-light photographs of the solar corona and in-situ measurements of the spaghetti-like fine-structure of high-speed winds.