Coronal seismology is now a well developed area of solar physics, even though many questions remain for resolution. Here we take stock of the progress made since the first direct imaging of oscillating loops was achieved through TRACE spacecraft observations in 1999.

The existence of the solar tachocline, a thin differentially rotating layer at the base of the convection zone which is inferred from helioseismology, leads to the concept of an interface dynamo. The tachocline is magnetically coupled to the radiative interior and the overlying convection zone. A multilayered interface dynamo is required to describe the dynamo process involved. We first discuss a two-dimensional multilayered interface dynamo model in cartesian geometry consisting of four horizontal layers with different magnetic diffusivities magnetically coupled by the three sets of interface matching conditions for the generated magnetic field. Exact solutions of the coupled dynamo system are obtained in this model. We then discuss a fully three-dimensional and multi-layered spherical dynamic interface dynamo using a finite element method based on the three-dimensional tetrahedralization of the whole spherical system. The spherical dynamic interface dynamo also consists of four magnetically coupled zones. In the convection zone, the fully three-dimensional dynamic feedback of Lorentz forces is taken into account. It is shown that the dynamo is characterized by a strong toroidal magnetic field, selects dipolar symmetry and propagates equatorward.

We briefly present recent simulations of the internal magnetism of the Sun with the 3-D ASH code and with the 2-D STELEM code. The intense magnetism of the Sun is linked to local and global dynamo action within our star. We focus our study on how magnetohydrodynamical processes in stable (radiative) or unstable (convective) zones, nonlinearly interact to establish the solar differential rotation, meridional circulation, confine the tachocline, amplify and organise magnetic fields and how magnetic flux emerge to the surface. We also test the robustness of flux transport dynamo models to various profiles of circulation.

Phase relations is extracted at different latitudes between the weak background solar magnetic (poloidal) field and strong magnetic field associated with sunspots (toroidal field) by comparing low-resolution images from Wilcox Solar Observatory (WSO) and the high-resolution SOHO/MDI magnetograms. Sunspot areas and excess flux in all latitudinal zones (averaged with a sliding 1 year filter) reveal a strong positive correlation with the absolute and excess solar magnetic fields with a timelag of zero and ∼ 3 years. The residuals of a sunspot magnetic excess flux averaged by one year from those by 4 years are shown to have well defined periodic temporal and spatial structures. The periods of these structures are close to π/4 (π≈ 11 years). The structures have maxima at −40^ and +40^ and reveal spatial drifts with time either towards the equator or the poles depending on a latitude of sunspot occurences.

Magneto-hydrodynamic wave modes propagating from the solar photosphere into the corona have the potential to be exploited as an observational tool in an analogous way to the use of acoustic waves in helio/terrestrial seismology. In regions of strong magnetic field photospheric p-modes are thought to undergo mode conversion to slow magneto-acoustic waves, and that these slow magnetoacoustic p-modes may be waveguided from the photosphere into the solar corona along the magnetic field. A Bayesian analysis technique is applied to observations which suggests four distinct p-modes may be resolved in the transition region.

We seek to clarify the nature of running penumbral (RP) waves: are they chromospheric trans-sunspot waves or a visual pattern of upward-propagating waves? Full Stokes spectropolarimetric time series of the photospheric Sii10827 Å line and the chromospheric Hei10830 Å multiplet were inverted using a Milne-Eddington code. Spatial pixels were paired between the outer umbral/inner penumbral photosphere and the penumbral chromosphere using inclinations retrieved by the inversion and the dual-height pairings of line-of-sight velocity time series were studied for signatures of wave propagation using a Fourier phase difference analysis. The dispersion relation for radiatively cooling acoustic waves, modified to incorporate an inclined propagation direction, fits well the observed phase differences between the pairs of photospheric and chromospheric pixels. We have thus demonstrated that RP waves are in effect low-β slow-mode waves propagating along the magnetic field.

The momenta and start times measured from the TD diagrams in 3 seismic sources observed in the flare of 28 October 2003 are compared with those delivered to the photosphere by different kinds of high energy particles as well as by the hydrodynamic shocks caused by these particles. The energetic protons with energy power laws combined with quasi-thermal ones are shown to form hydrodynamic shocks deeply in a flaring atmosphere which deliver the required momentum to the photosphere within a measured timescale. The seismic waves observed in two sources associated with γ-rays can be explained by the momenta produced by hydrodynamic shocks caused by mixed proton beams and jets. The seismic wave in the source asociated with HXR only and delayed by 4 and 2 minutes from the first and second HXR bursts is likely to be associated with a hydrodynamic shock occurring from precipitation of a very powerful and hard electron beam possibly mixed with quasi-thermal lower energy protons.

The chromosphere of the quiet Sun is a highly intermittent and dynamic phenomenon. Three-dimensional radiation (magneto-)hydrodynamic simulations exhibit a mesh-like pattern of hot shock fronts and cool expanding post-shock regions in the sub-canopy part of the inter-network. This domain might be called “fluctosphere”. The pattern is produced by propagating shock waves, which are excited at the top of the convection zone and in the photospheric overshoot layer. New high-resolution observations reveal a ubiquitous small-scale pattern of bright structures and dark regions in-between. Although it qualitatively resembles the picture seen in models, more observations – e.g. with the future ALMA – are needed for thorough comparisons with present and future models. Quantitative comparisons demand for synthetic intensity maps and spectra for the three-dimensional (magneto-)hydrodynamic simulations. The necessary radiative transfer calculations, which have to take into account deviations from local thermodynamic equilibrium, are computationally very involved so that no reliable results have been produced so far. Until this task becomes feasible, we have to rely on careful qualitative comparisons of simulations and observations. Here we discuss what effects have to be considered for such a comparison. Nevertheless we are now on the verge of assembling a comprehensive picture of the solar chromosphere in inter-network regions as dynamic interplay of shock waves and structuring and guiding magnetic fields.

We present an observational test of the hypothesis that leaking p modes heat the solar chromosphere. The amplitude of the leaking p modes in magneto-acoustic portals is determined using MOTH and MDI data. We simulate the propagation of these modes into the chromosphere to determine the height where the wave energy is dissipated by shock waves. A statistical approach is then used to check if this heating process could account for the observed variability of the intensity in the Lyman-α emission.

The aim of this work is to examine the hypothesis that the wave propagation time in the solar atmosphere can be used to infer the magnetic topography in the chromosphere as suggested by Finsterle et al. (2004). We do this by using an extension of our earlier 2-D MHD work on the interaction of acoustic waves with a flux sheet. It is well known that these waves undergo mode transformation due to the presence of a magnetic field which is particularly effective at the surface of equipartition between the magnetic and thermal energy density, the β = 1 surface. This transformation depends sensitively on the angle between the wave vector and the local field direction. At the β = 1 interface, the wave that enters the flux sheet, (essentially the fast mode) has a higher phase speed than the incident acoustic wave. A time correlation between wave motions in the non-magnetic and magnetic regions could therefore provide a powerful diagnostic for mapping the magnetic field in the chromospheric network.

This investigation is a continuation of earlier work on the dynamics of the magnetic network. In a previous calculation (Hasan et al. 2005), we examined the response of a single flux tube to transverse motions of its footpoints. We now extend this analysis to a more realistic model of the network consisting of multiple flux tubes. We apply a transverse velocity perturbation uniformly along the lower boundary located at the base of the photosphere. Our 2-D MHD simulations enable us to study the complex wave pattern due to waves generated in the individual tubes as well as their interaction with those emanating from adjacent tubes. Our results show that the dominant heating of the chromosphere occurs due to slow magnetoacoustic waves in a region that is close to the central region of the flux tube.

The upward propagation of linear acoustic waves in a gravitationally stratified atmosphere is studied. The wave motion is governed by the Klein-Gordon equation which contains a cut-off frequency introduced by stratification. The acoustic cut-off may act as a potential barrier when the temperature decreases with height. It is shown that waves trapped below the barrier could be subject to a resonance which extends into the entire unbounded atmosphere. The parameter space characterizing the resonance is explored.

The quiet solar chromosphere in regions with negligible magnetic field is believed to be heated by acoustic waves. But their energy flux, measured in the upper photosphere with the Transition Region And Coronal Explorer (TRACE), has been found to be insufficient to account for the radiative emission from the chromosphere. Wedemeyer-Böhm et al. (2007) and Cuntz et al. (2007), employing a 3D hydrodynamical model by Wedemeyer et al. (2004), have proposed that the spatial resolution of TRACE is inadequate to resolve intensity fluctuations that occur on small spatial scales. This paper accepts the principle of spatial averaging by TRACE as a qualitative explanation for the low acoustic flux but finds that the hydrodynamical model is too much simplified in the treatment of radiative energy exchange to provide a quantitative measure of the suppression of the fluctuations. The heating mechanism of the chromosphere thus remains an open question.

Multi-wavelength studies of energetic solar flares with seismic emissions have revealed interesting common features that may help us to identify the correlations of flare signatures from the inner to the outer solar atmosphere and, to develop diagnostic techniques to aid in the sun quake detection. In our study, we make use the relation between the microwave and the hard X-ray emissions associated with such flares to propose a scenario for the ignition of seismic transients from flares. We explore the mechanisms of energy transport to the photosphere, such us back-warming or direct particle impacts.

The observations of sunspot chromosphere are presented. The authors suggest the existence of two modes of propagating waves at the chromospheric level. The connection between these modes and magnetic field topology can be inferred from the analysis of mode propagation velocity and spatial localization. Two hypotheses are tested to explain the phenomenon: “Visual pattern” and “Trans-sunspot wave”.

We have analysed the 6 mHz egression power signatures of some accoustically active X-class solar flares. During the impulsive phase these flares produced conspicuous seismic signatures which have kernel-like structures, mostly aligned with the neutral line of the host active region. The kernel-like structures show the effect of constructive interference of the acoustic waves emanating from the complex sources, suggesting motion of the acoustic sources. The co-aligment between the seismic signatures and the hard X-ray emission observed by RHESSI from the footpoints of the coronal loops suggests a direct link between relativistic particles accelerated during the flare and the hydrodynamic response of the photosphere during flares.

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.

The extreme-ultraviolet (EUV) imagers onboard the planned Solar Dynamics Observatory (SDO) and Solar Orbiter (SO) will offer us the best chance yet of using observations of post-flare loop oscillations to probe the fine structure of the corona. Recently developed magnetohydrodynamic (MHD) wave theory has shown that the properties of loop oscillations depend on their plasma fine structure. Up to this point, many studies have concentrated solely on the effect of plasma density stratification on coronal loop oscillations. In this paper we develop MHD wave theory which models the effect of an inhomogeneous magnetic field on coronal loop oscillations. The results have the potential to be used in testing the efficacy of photospheric magnetic field extrapolations and have important implications regarding magneto-seismology of the corona.

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.

TRACE observations (23/11/1998 06:35:57-06:48:43UT) in the 171 Å bandpass of an active region are studied. Coronal loop oscillations are observed after a violent disruption of the equilibrium. The oscillation properties are studied to give seismological estimates of physical quantities, such as the density scale height. A loop segment is traced during the oscillation, and the resulting time series is analysed for periodicities. In the loop segment displacement, two periods are found: 435.6±4.5 s and 242.7±6.4 s, consistent with the periods of the fundamental and 2nd harmonic fast kink oscillation. The small uncertainties allow us to estimate the density scale height in the loop to be 109 Mm, which is about double the estimated hydrostatical value of 50 Mm. The eigenfunction is used to do spatial coronal seismology, but that method does not give any conclusive results.