With modern imaging and spectral instruments observing in the visible, EUV, X-ray, and radio wavelengths, the detection of oscillations in the solar outer atmosphere has become a routine event. These oscillations are considered to be the signatures of a wave phenomenon and are generally interpreted in terms of magnetohydrodynamic (MHD) waves. With multiwavelength observations from ground-and space-based instruments, it has been possible to detect waves in a number of different wavelengths simultaneously and, consequently, to study their propagation properties. Observed MHD waves propagating from the lower solar atmosphere into the higher regions of the magnetized corona have the potential to provide excellent insight into the physical processes at work at the coupling point between these different regions of the Sun. High-resolution wave observations combined with forward MHD modeling can give an unprecedented insight into the connectivity of the magnetized solar atmosphere, which further provides us with a realistic chance to reconstruct the structure of the magnetic field in the solar atmosphere. This type of solar exploration has been termed atmospheric magnetoseismology. In this review we will summarize some new trends in the observational study of waves and oscillations, discussing their origin and their propagation through the atmosphere. In particular, we will focus on waves and oscillations in open magnetic structures (e.g., solar plumes) and closed magnetic structures (e.g., 4 D. Banerjee et al. loops and prominences), where there have been a number of observational highlights in the past few years. Furthermore, we will address observations of waves in filament fibrils allied with a better characterization of their propagating and damping properties, the detection of prominence oscillations in UV lines, and the renewed interest in large-amplitude, quickly attenuated, prominence oscillations, caused by flare or explosive phenomena.

From recent high resolution observations obtained with the Swedish 1-m Solar Telescope in La Palma, we detect swaying motions of individual filament threads in the plane of the sky. The oscillatory character of these motions are comparable with oscillatory Doppler signals obtained from corresponding filament threads. Simultaneous recordings of motions in the line-of-sight and in the plane of the sky give information about the orientation of the oscillatory plane. These oscillations are interpreted in the context of the magnetohydrodynamic theory. Kink magnetohydrodynamic waves supported by the thread body are proposed as an explanation of the observed thread oscillations. On the basis of this interpretation and by means of seismological arguments, we give an estimation of the thread Alfvén speed and magnetic field strength by means of seismological arguments.

First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range.

Aims. The role of collisions between ions, electrons and neutrals in a partially ionised plasma is assessed as a possible wave damping mechanism. The relevance of this mechanism in the damping of small amplitude prominence oscillations is evaluated. Methods. A one-fluid MHD set of equations taking into account various effects in a partially ionised solar plasma (collisions between different species and Joule dissipation) is derived. Assuming small perturbations, these equations are next linearised about a uniform equilibrium configuration and the dispersion relation of magnetoacoustic waves in an unbounded medium is obtained.Results. The presence of neutrals in the plasma only affects the fast wave in a relevant way. An approximate expression for the damping rate is obtained which shows that the strongest damping takes place in a medium with strong magnetic field, low density and low ionisation fraction. Wave attenuation arises mostly from collisions between ions and neutrals. Conclusions. Given the poor knowledge about the values of the density and ionisation fraction in prominences, it is hard to judge the importance of the physics of partial ionisation in the damping of fast waves in solar prominences. Nevertheless, note that a very idealised case, with no stratification and no equilibrium currents, is considered here, so the addition of these features to the model may change the results of this work.

Abstract. Using time series of two-dimensional Dopplergrams, a temporal and spatial analysis of oscillations in a quiescent prominence has been performed. The presence of an outstanding oscillatory signal in the acquired data has allowed us to study the two-dimensional distribution of wave motions and, in particular, to detect the location of wave generation and the anisotropic propagation of perturbations from that place. Moreover, a strong damping of oscillations has been observed, with damping times between two and three times the wave period. The direction of propagation, wavelength and phase speed, together with the damping time and wave period, have been quantified and their spatial arrangement has been analysed. Thanks to the goodness of the observational data, the image alignment procedure applied during the data reduction stage and the analysis tools employed, it has been possible to carry out a novel and far-reaching observational study of prominence oscillations.

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Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and are compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences. Subject headings: Sun: oscillations -Sun: atmosphere -Sun: magnetic fields -waves -Magnetohydrodynamics (MHD) omit the intermediate steps and give the final expression of the dispersion relation, namely k ⊥,e ρ e ω 2 −k 2 z v 2 A,e K ′ m [k⊥,e(R+l/2)] K m[ k ⊥,e (R+l/2)] G e − Ξ e k ⊥,e ρ e ω 2 −k 2 z v 2 A,e K ′ m[ k ⊥,e (R+l/2)] K m[ k ⊥,e (R+l/2)] F e − Γ e

Prominences are intriguing, but poorly understood, magnetic structures of the solar corona. The dynamics of solar prominences has been the subject of a large number of studies, and of particular interest is the study of prominence oscillations. Ground-and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences) that are difficult to measure by direct means. Here, we review the observational information gathered about prominence oscillations as well as the theoretical models developed to interpret small amplitude oscillations and their temporal and spatial attenuation. Finally, several prominence seismology applications are presented.