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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, two prominence seismology applications are presented.

© ESO 2019. The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic waves in coronal loops is better referred to as a reduced seismological problem. "Reduced" emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions. ispartof: ASTRONOMY & ASTROPHYSICS vol:622 status: published

We study the excitation and damping of transverse oscillations in a complex multi-stranded model of a coronal loop. By numerically solving the time-dependent magnetohydrodynamic (MHD) equations in two dimensions, we show how the global motion of the whole bundle of tubes, produced by an external disturbance, is converted into localised motions due to the process of resonant absorption. At any location in the structure two dominant frequencies are found, the frequency of the global mode (different from the kink frequency of the individual strands) and the local Alfvén frequency. The mechanism of mode conversion is not affected by the complicated geometry of the system and for certain configurations the energy conversion does not only take place at the external edge of the composite loop but also inside the structure.

We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modelled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping due to resonant absorption is computed. Due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected.

We study the effects of magnetic field shear (B y ¬= 0) and longitudinal propagation of perturbations (k y ¬= 0) on the linear and adiabatic magnetohydrodynamic (MHD) normal modes of oscillation of a potential coronal arcade. In a cold plasma, the inclusion of these two effects produces the linear coupling of discrete fast modes, characterised by a discrete spectrum of frequencies and a global velocity structure, and Alfven continuum modes, characterised by a continuous spectrum of frequencies and with a velocity perturbation confined to given magnetic surfaces in such a way that modes with mixed properties arise (Arregui et al. 2004). The wave equations governing the velocity perturbations have been solved numerically and our results show that the couplings between fast and Alfven modes are governed by some parity rules for the symmetry of the eigenfunctions of fast and Alfven modes in the direction along the equilibrium magnetic field. The nature of the coupling between fast and Alfven modes can be resonant or non-resonant depending on the location of the fast mode frequency within the different Alfven continua. Also, an important result is that in this kind of configurations coupled modes could be difficult to observe since when both magnetic field shear and longitudinal propagation are present the spatial distribution of the velocity may not be confined to low heights in the solar corona.

The magnetohydrodynamic (MHD) normal modes of oscillation of sheared coronal arcades including longitudinal wave propagation are studied. Solutions have been computed to ascertain the effects of the longitudinal magnetic field component, By, and of the longitudinal wavenumber, ky, in these structures. Our results show that whenever By ≠ 0 and/or ky ≠ 0, fast modes, characterized by a global velocity structure and a discrete spectrum of frequencies, and Alfven continuum modes, characterized by a velocity perturbation confined to given magnetic surfaces, get coupled and no pure fast modes or pure Alfven modes exist, but modes with mixed properties arise. These oscillatory modes display a global spatial distribution, together with a nonsquare integrable singular behavior on certain magnetic surfaces. Moreover, this mode coupling is such that under some circumstances the Alfvenic contribution is also in the form of a smooth velocity profile covering a range of magnetic surfaces instead of a singularity on a fixed magnetic surface. The coupling between fast and Alfven modes is governed by the parity of their eigenfunctions in the direction along the equilibrium magnetic field. The parity rules determining the features of coupled modes in terms of their spatial structure, ky, and By are presented. We have found that the frequency of coupled modes is real when either By ≠ 0 or ky ≠ 0 but is complex when both By ≠ 0 and ky ≠ 0. Also, an important result is that coupled modes may not be observable since many of them leak energy away from the solar corona.

The theoretical understanding of the linear standing or propagating magnetohydrodynamic waves in a variety of solar coronal structures is far from complete since analytical solutions to the linearised MHD equations can only be found for very simple magnetic configurations. In this paper, we use a numerical code to solve the linear fast and Alfven wave equations in a very simple, bounded magnetic configuration that incorporates two features that are not usually considered in similar works, namely the longitudinal magnetic field component and wave propagation in the longitudinal direction ($k_y\neq 0$). We use a numerical code (Arregui et al. 2001) that has been modified by including a staggered mesh that allows us to properly capture the spatial behaviour of solutions to the wave equations. Coupling between fast and Alfven modes has been studied in detail and it has been found that it does not take place when the longitudinal field component is zero and the frequency of the fast mode is outside the Alfven continuum with the same spatial structure along field lines. Under these circumstances, fast modes retain their global spatial behaviour and are also characterised by $\omega^2$ varying linearly with $k_y^2$, such as in a uniform medium (although here the Alfven speed changes exponentially in the direction normal to field lines). Regarding mode coupling, its main feature is the blend of fast and Alfven solutions with close frequencies in some modes with a mixture of their properties, namely discontinuities or jumps around certain magnetic surfaces (such as in pure Alfven waves), global spatial distribution of the normal velocity component and non-zero density perturbations (such as in fast waves).

High resolution observations of the solar corona made with instruments onboard the SOHO and TRACE spacecrafts have provided new evidence for the presence of oscillations in a variety of coronal magnetic structures. Most of these observations have been interpreted in terms of linear standing or propagating magnetohydrodynamic (MHD) waves, but the theoretical understanding is far from complete since analytical solutions to the linearised MHD wave equations can only be found for very simple magnetic congurations. Taking into account that the solar corona is basically structured by force-free magnetic elds, our purpose in this paper is to present the derivation of the linear MHD wave equations for a two-dimensional force-free magnetic eld conguration having longitudinal invariance, as well as to introduce a numerical code to solve the resulting system of coupled partial dierential equations. The accuracy of the code has been checked by numerically solving two cases for which analytical or simple numerical solutions exist. To our knowledge, this is the only two-dimensional code developed to study the normal MHD modes of oscillation of a general force-free eld with longitudinal invariance.

Observations show that propagating magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. The technique of MHD seismology uses the wave observations combined with MHD wave theory to indirectly infer physical parameters of the solar atmospheric plasma and magnetic field. Here we present an analytical seismological inversion scheme for propagating MHD waves. This scheme uses in a consistent manner the observational information on wavelengths and damping lengths, along with observed values of periods or phase velocities, and is based on approximate asymptotic expressions for the theoretical values of wavelengths and damping lengths. The applicability of the inversion scheme is discussed and an example is given.