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.     

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.     

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.     

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.     

Oscillations and Waves in Solar Spicules

Since their discovery, spicules have attracted increased attention as energy/mass bridges between the dense and dynamic photosphere and the tenuous hot solar corona. Mechanical energy of photospheric random and coherent motions can be guided by magnetic field lines, spanning from the interior to the upper parts of the solar atmosphere, in the form of waves and oscillations. Since spicules are one of the most pronounced features of the chromosphere, the energy transport they participate in can be traced by the observations of their oscillatory motions. Oscillations in spicules have been observed for a long time. However the recent high-resolution and high-cadence space and ground based facilities with superb spatial, temporal and spectral capacities brought new aspects in the research of spicule dynamics. Here we review the progress made in imaging and spectroscopic observations of waves and oscillations in spicules. The observations are accompanied by a discussion on theoretical modelling and interpretations of these oscillations. Finally, we embark on the recent developments made on the presence and role of Alfvén and kink waves in spicules. We also address the extensive debate made on the Alfvén versus kink waves in the context of the explanation of the observed transverse oscillations of spicule axes.     

Alfvén Waves in the Solar Atmosphere

Alfvén waves are considered to be viable transporters of the non-thermal energy required to heat the Sun’s quiescent atmosphere. An abundance of recent observations, from state-of-the-art facilities, have reported the existence of Alfvén waves in a range of chromospheric and coronal structures. Here, we review the progress made in disentangling the characteristics of transverse kink and torsional linear magnetohydrodynamic (MHD) waves. We outline the simple, yet powerful theory describing their basic properties in (non-)uniform magnetic structures, which closely resemble the building blocks of the real solar atmosphere.     

EIT Waves: A Changing Understanding over a Solar Cycle

We present here a review of observations and the current theories that attempt to explain coronal EIT waves. EIT waves were first observed by SOHO-EIT in 1996. Since then, careful analysis has shown that they are related to various other phenomena, such as: CMEs, coronal dimming regions, Moreton waves, and transverse coronal loop oscillations. Over the years, myriad theories have been proposed to explain EIT waves. Early attempts, while elegant, relied heavily on theories based on pre-coronal observations. More recent work, which tends to consider a larger data pool, has led to two competing theoretical camps: wave vs. non-wave models; in many cases, proposed hypotheses flatly contradict each other. Sifting through these seemingly-incongruous models requires a thorough understanding of the available data, as some observations make certain theories more difficult to justify. However, some questions still do not appear resolvable with current data and will likely require help from the next generation of coronal telescopes.     

MHD waves in coronal flux tubes

The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona.     

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 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.     

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.     

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.     

Short Quasi-Periodic MHD Waves in Coronal Structures

The possibility of remote diagnostics of coronal structures with impulsively-generated short-period fast magnetoacoustic wave trains is demonstrated. An initially broad-band, aperiodic fast magnetoacoustic perturbation guided by a 1D plasma inhomogeneity develops into a quasi-periodic wave train with a well-pronounced frequency and amplitude modulation. The quasi-periodicity results from the geometrical dispersion of the modes, determined by the transverse profile of the loop, and hence contains information about the profile. Wavelet images of the wave train demonstrate that their typical spectral signature is of a “crazy tadpole’’ shape: a narrow spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time, with a mean value of several seconds for typical coronal values. The period and the spectral amplitude evolution are determined by the steepness of the transverse density profile and the density contrast ratio in the loop, which offers a tool for estimation of the sub-resolution structuring of the corona.     

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.     

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.     

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.     

Mass flows in coronal loops

Although static loop models are often used to describe the structure of coronal loops, it is evident on both observational and theoretical grounds that mass motions play a crucial role in the physics of the corona and transition region. First we review the observations of emission-line broadening and wavelength shifts, which imply the presence of random motions and systematic downflows in coronal loops. Some discrepancies in the observations are discussed. It is argued that velocities due to gas pressure gradients are the most likely explanation for the observed flows. A number of models that have been proposed for these motions are reviewed. The implications of the various models on observations of the corona and transition region by SOHO are discussed.     

Element and Isotopic Fractionation in Closed Magnetic Structures

Recent papers have suggested that the slow solar wind is a super-position of material which is released by reconnection from large coronal loops. This reconnection process is driven by large-scale motions of solar magnetic flux driven by the non-radial expansion of the solar wind from the differentially rotating photosphere into more rigidly rotating coronal holes. The elemental composition of the slow solar wind material is observed to be fractionated and more variable than the fast solar wind from coronal holes. Recently, it has also been reported that fractionation also occurs in 3He/4He. This may be interpreted in the frame-work of an existing model for fractionation on large coronal loops in which wave-particle interactions preferentially heat ions thereby modifying their scale-heights. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

Short Timescale Core Dynamics: Theory and Observations

Fluid motions in the Earth’s core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet’s rotational dynamics. In this article we review current understanding of core dynamics focusing on short timescales of years to centuries. We describe both theoretical models and what may be inferred from geomagnetic and geodetic observations. The kinematic concepts of frozen flux and magnetic diffusion are discussed along with relevant dynamical regimes of magnetostrophic balance, tangential geostrophy, and quasi-geostrophy. An introduction is given to free modes and waves that are expected to be present in Earth’s core including axisymmetric torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We focus on important recent developments and promising directions for future investigations.