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.     

Excitation of Standing Kink Oscillations in Coronal Loops

In this work we review the efforts that have been done to study the excitation of the standing fast kink body mode in coronal loops. We mainly focus on the time-dependent problem, which is appropriate to describe flare or CME induced kink oscillations. The analytical and numerical studies in slab and cylindrical loop geometries are reviewed. We discuss the results from very simple one-dimensional models to more realistic (but still simple) loop configurations. We emphasise how the results of the initial value problem complement the eigenmode calculations. The possible damping mechanisms of the kink oscillations are also discussed.     

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.     

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.     

Longitudinal Waves in Coronal Loops

Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers.     

Propagating MHD Waves in Coronal Holes

Coronal holes are the coolest and darkest regions of the upper solar atmosphere, as observed both on the solar disk and above the solar limb. Coronal holes are associated with rapidly expanding open magnetic fields and the acceleration of the high-speed solar wind. During the years of the solar minima, coronal holes are generally confined to the Sun??s polar regions, while at solar maxima they can also be found at lower latitudes. Waves, observed via remote sensing and detected in-situ in the wind streams, are most likely responsible for the wind and several theoretical models describe the role of MHD waves in the acceleration of the fast solar wind. This paper reviews the observational evidences of detection of propagating waves in these regions. The characteristics of the waves, like periodicities, amplitude, speed provide input parameters and also act as constraints on theoretical models of coronal heating and solar wind acceleration.     

The 3D Geometry, Motion, and Hydrodynamic Aspects of Oscillating Coronal Loops

We transition from two-dimensional (2D) imaging observations of kink-mode loop oscillations in the solar corona to three-dimensional (3D) reconstructions by exploring two new methods: (1) De-projection of 2D loop tracings using the strategy of curvature radius maximization in 3D space, based on the assumption of force-free magnetic fields; and (2) stereoscopic triangulation of epipolar loop coordinates using coaligned images from the STEREO EUVI/A and B spacecraft. Both methods reveal new features of oscillating loops: non-circularity, non-planarity, and helical geometries. We extend the 3D reconstruction techniques into the time domain and find indications of circularly polarized (helical) kink-mode oscillations, in contrast to linearly polarized modes assumed previously. We discuss also hydrodynamic effects of coronal loops in non-equilibrium state that are essential for the detection and modeling of kink-mode 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.     

Coronal mass ejections at high heliographic latitudes: Ulysses

Nine coronal mass ejections (CMEs) have been detected in the solar wind by the Ulysses plasma experiment between 31° and 61° South. One of these events, which was also a magnetic cloud, was directly associated with an event observed by the soft X-ray telescope on Yohkoh in which large magnetic loops formed in the solar corona directly beneath Ulysses. This association suggests that the flux rope topology of the magnetic cloud resulted from reconnection between the legs of neighboring magnetic loops within the rising CME. The average CME speed (740 km s^–1) at these latitudes was comparable to that of the normal solar wind there and is much greater than average CME speeds observed either in the solar wind in the ecliptic plane or in the corona close to the Sun. We suggest that the same basic acceleration process applies to both slow CMEs and the normal solar wind at any latitude.     

Coronal Heating by Magnetic Explosions

From magnetic fields and coronal heating observed in flares, active regions, quiet regions, and coronal holes, we propose that exploding sheared core magnetic fields are the drivers of most of the dynamics and heating of the solar atmosphere, ranging from the largest and most powerful coronal mass ejections and flares, to the vigorous microflaring and coronal heating in active regions, to a multitude of fine-scale explosive events in the magnetic network, driving microflares, spicules, global coronal heating, and, consequently, the solar wind. This revised version was published online in June 2006 with corrections to the Cover Date.     

Coronal Seismology by Means of Kink Oscillation Overtones

The detection of overtones of coronal loop kink oscillations has been an important advance in the development of coronal seismology. It has significantly increased the potential of coronal seismology and has thus initiated important theoretical and observational improvements. New detections of overtones have been made and a reduction of the error bars has been obtained. The efforts of theoreticians to extend eigenmode studies to more general coronal loop models is no longer a matter of checking the robustness of the model but now also allows for the estimation of certain equilibrium parameters. The frequencies of the detected (longitudinal) overtones are in particular sensitive to changes in the equilibrium properties along the loop, especially the density and the magnetic field expansion. Also, attempts have been made to use the limited longitudinal resolution in combination with the theoretical eigenmodes as an additional seismological tool.     

Abundances,Ionization States,Temperatures, and FIP in Solar Energetic Particles

The relative abundances of chemical elements and isotopes have been our most effective tool in identifying and understanding the physical processes that control populations of energetic particles. The early surprise in solar energetic particles (SEPs) was 1000-fold enhancements in \({}^{3}\mbox{He}/{}^{4}\mbox{He}\) from resonant wave-particle interactions in the small “impulsive” SEP events that emit electron beams that produce type III radio bursts. Further studies found enhancements in Fe/O, then extreme enhancements in element abundances that increase with mass-to-charge ratio \(A/Q\), rising by a factor of 1000 from He to Au or Pb arising in magnetic reconnection regions on open field lines in solar jets. In contrast, in the largest SEP events, the “gradual” events, acceleration occurs at shock waves driven out from the Sun by fast, wide coronal mass ejections (CMEs). Averaging many events provides a measure of solar coronal abundances, but \(A/Q\)-dependent scattering during transport causes variations with time; thus if Fe scatters less than O, Fe/O is enhanced early and depleted later. To complicate matters, shock waves often reaccelerate impulsive suprathermal ions left over or trapped above active regions that have spawned many impulsive events. Direct measurements of ionization states \(Q\) show coronal temperatures of 1–2 MK for most gradual events, but impulsive events often show stripping by matter traversal after acceleration. Direct measurements of \(Q\) are difficult and often unavailable. Since both impulsive and gradual SEP events have abundance enhancements that vary as powers of \(A/Q\), we can use abundances to deduce the probable \(Q\)-values and the source plasma temperatures during acceleration, ≈3 MK for impulsive SEPs. This new technique also allows multiple spacecraft to measure temperature variations across the face of a shock wave, measurements otherwise unavailable and provides a new understanding of abundance variations in the element He. Comparing coronal abundances from SEPs and from the slow solar wind as a function of the first ionization potential (FIP) of the elements, remaining differences are for the elements C, P, and S. The theory of the fractionation of ions by Alfvén waves shows that C, P, and S are suppressed because of wave resonances during chromospheric transport on closed magnetic loops but not on open magnetic fields that supply the solar wind. Shock waves can accelerate ions from closed coronal loops that easily escape as SEPs, while the solar wind must emerge on open fields.     

Large-scale Coronal Heating, Clustering of Coronal Bright Points, and Concentration of Magnetic Flux

By combining quiet-region Fe XII coronal images from SOHO/EIT with magnetograms from NSO/Kitt Peak and from SOHO/MDI, we show that the population of network coronal bright points and the magnetic flux content of the network are both markedly greater under the bright half of the large-scale quiet corona than under the dim half. These results (1) support the view that the heating of the entire corona in quiet regions and coronal holes is driven by fine-scale magnetic activity (microflares, explosive events, spicules) seated low in the magnetic network, and (2) suggest that this large-scale modulation of the magnetic flux and coronal heating is a signature of giant convection cells. This revised version was published online in June 2006 with corrections to the Cover Date.     

Coronal heating by dissipation of magnetic structure

Coronal loops are heated by the release of stored magnetic energy and by the dissipation of MHD waves. Both of these processes rely on the presence of internal structure in the loop. Tangled or sheared fields dissipate wave energy more efficiently than smooth fields. Also, a highly structured field contains a large reservoir of free magnetic energy which can be released in small reconnection events (microflares and nanoflares). The typical amount of internal structure in a loop depends on the balance between input at the photosphere and dissipation. This paper describes measures of magnetic structure, how these measures relate to the magnetic energy, and how photospheric motions affect the structure of a loop.The magnetic energy released during a reconnection event. can be estimated if one knows the equilibrium energy before and after the event. For a loop with highly tangled field lines, a direct solution of the equilibrium equations may be difficult. However, lower bounds can be placed on the energy of the equilibrium field, given a measure of the tangling known as the crossing number. These bounds lead to an estimate of the buildup of energy in a coronal loop caused by random photospheric motions. Parker's topological dissipation model can plausibly supply the 10⁷ erg cm^–2 s^–1 needed to heat the active region corona. The heating rate can be greatly enhanced by fragmentation of flux tubes, for example by the breakup of photospheric footpoints and the formation of new footpoints.     

The Effect of Loop Curvature on Coronal Loop Kink Oscillations

We will review analytical and numerical efforts in modelling the influence of curvature on coronal loop oscillations. We will mainly focus our attention on fast kink mode oscillations. A curved slab model will be presented, where it becomes clear that curvature introduces wave leakage into the system, because of changes in the equilibrium. The importance of leakage will be assessed through the use of a slab and cylindrical model where lateral leakage is allowed. A full analytical model for a semi-toroidal loop will be constructed for a system with no leaking waves but with an inhomogeneous layer that introduces damping due to the process of resonant absorption. The model for a semi-toroidal loop will be extended to also include leakage, and will be studied numerically. The numerical results will be compared to the analytical model.     

Heating Diagnostics with MHD Waves

The heating of the solar atmosphere is a fundamental problem of modern solar and astrophysics. A review of the seismological aspects of magnetohydrodynamic (MHD) waves with an emphasis on standing longitudinal waves in the context of coronal heating is presented. Efforts made recently may be split into two categories: forward modelling and data inversion. Forward modelling can be applied to predict the observational footprints of various heating scenarios. A new diagnostic method based on the analysis of Doppler shift time series is outlined with specific application to solar coronal conditions. The power of the method is demonstrated and tested using synthetic data and comparing them with actual high-resolution (e.g. SoHO/SUMER) observations. Further, related recent examples of standing longitudinal oscillations in coronal loop structures observed with the new Hinode/EIS instrument are also presented. These latter observations provide an advanced ground for MHD seismology as a tool for plasma heating diagnostics in the atmosphere of the Sun.     

On the Slow Solar Wind

A theory for the origin of the slow solar wind is described. Recent papers have demonstrated that magnetic flux moves across coronal holes as a result of the interplay between the differential rotation of the photosphere and the non-radial expansion of the solar wind in more rigidly rotating coronal holes. This flux will be deposited at low latitudes and should reconnect with closed magnetic loops, thereby releasing material from the loops to form the slow solar wind. It is pointed out that this mechanism provides a natural explanation for the charge states of elements observed in the slow solar wind, and for the presence of the First-Ionization Potential, or FIP, effect in the slow wind and its absence in fast wind. Comments are also provided on the role that the ACE mission should have in understanding the slow solar wind. This revised version was published online in June 2006 with corrections to the Cover Date.     

3D Coronal structures and their evolutions measured by Stereoscopy,consequences for Space Weather and the STEREO mission

We are discussing methods of stereoscopic 3D reconstruction of coronal loops structures. In our most sophisticated method we fit loops observed with SOHO/EIT to a set of shape parameters including the internal twist of the loops field lines. We define this twist as the number of turns of the field line around a torus axis between the footpoints of the loops. Twist numbers of the order 0–2 are observed. We observe the emergence of an Active Region with twisted loops which detwist as they expand. The same correlation between detwisting and expansion is observed with filaments in relation to CME formations. On longer time scale, loops seem to accumulate twist, perhaps due to differential rotation. Rapid losses of twist temporarily correlate with flares. From our analysis, we expect that the internal twist of coronal structures will play an important role for the space weather forecast. This revised version was published online in August 2006 with corrections to the Cover Date.     

MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.     

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.