J. L. Ballester

On the nature of kink MHD waves in magnetic flux tubes

Context. Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfven. The possibility that these waves have mixed properties is often ignored. Aims. The goal of this work is to study and determine the nature of MHD kink waves. Methods. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma which allows for MHD radiation. Results. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to (kzR) 2 . In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfven frequency, i.e. in the resonant layer. Conclusions. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfvenic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box.

OSCILLATIONS IN QUIESCENT SOLAR PROMINENCES OBSERVATIONS AND THEORY – (Invited Review)

An extensive observational background about the existence of oscillations in quiescent solar prominences has been gathered during the last twenty years. From these observations, information about different oscillatory parameters such as period, wavelength, phase speed, damping time, etc., has been obtained. This observational background, combined with a growing number of theoretical studies about magneto-hydrodynamic waves in prominences, should allow the development of prominence seismology which, following helioseismologys approach, seeks to infer the internal structure and properties of solar prominences. The most recent observational and theoretical developments on prominence oscillations are reviewed here, with an emphasis on the aspects suitable to develop an observation versus theory feedback, but also pointing out key topics which should be the subject of future research for a further advancement of this field.

Two-dimensional distribution of oscillations in a quiescent solar prominence

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.

Analytic approximate seismology of transversely oscillating coronal loops

Aims. We present an analytic approximate seismic inversion scheme for damped transverse coronal loop oscillations based on the thin tube and thin boundary approximation for computing the period and the damping time. Methods. Asymptotic expressions for the period and damping rate are used to illustrate the process of seismological inversion in a simple and easy to follow manner. The inversion procedure is formulated in terms of two simple functions, which are given by simple closed expressions. Results. The analytic seismic inversion shows that an infinite amount of 1-dimensional equilibrium models can reproduce the observed periods and damping times. It predicts a specific range of allowable values for the Alfven travel time and lower bounds for the density contrast and the inhomogeneity length scale. When the results of the present analytic seismic inversion are compared with those of a previous numerical inversion, excellent agreement is found up to the point that the analytic seismic inversion emerges as a tool for validating results of numerical inversions. Actually it helped us to identify and correct inaccuracies in a previous numerical investigation.

Damped Coronal Loop Oscillations: Time-dependent Results

The excitation and damping of transverse coronal loop oscillations is studied using a one-dimensional model of a line-tied cylindrical loop. By solving the time-dependent magnetohydrodynamic (MHD) equations, we show how an initial disturbance produced in the solar corona induces kink-mode oscillations. We analyze the effect of the disturbance on a loop with a nonuniform boundary layer and investigate the damping of such a disturbance due to resonant absorption. We find that the period and attenuation time of the time-dependent results agree with the calculations of the corresponding quasi-mode (i.e., the kink mode resonantly coupled to Alfven modes) and that the resonant absorption mechanism is capable of damping the oscillations almost immediately after the excitation. We study in detail the behavior of solutions in the inhomogeneous layer and show how the energy of the global oscillation is converted into torsional oscillations in the inhomogeneous layer. In addition, we estimate that the amplitude of the torsional oscillations is, for large magnetic Reynolds numbers and for thick layers, between 4 and 6 times the amplitude of the initial transverse motions. The implications of these results and their relationship with the observations are discussed.

Resonant Absorption in Complicated Plasma Configurations: Applications to Multistranded Coronal Loop Oscillations

We study the excitation and damping of transverse oscillations in a multistranded model of a straight line-tied coronal loop. The transverse geometry of our equilibrium configuration is quite irregular and more realistic than the usual cylindrical loop model. By numerically solving the time-dependent ideal magnetohydrodynamic equations in two dimensions, we show how the global motion of the whole bundle of strands, excited by an external disturbance, is converted into localized Alfv?nic motions due to the process of resonant absorption. This process produces the attenuation of the transverse oscillations. At any location in the structure, two dominant frequencies are found: the frequency of the global mode or quasi-mode, and the local Alfv?n frequency. We find that the mechanism of mode conversion, due to the coupling between fast and Alfv?n waves, is not compromised by the complicated geometry of the model. We also show that it is possible to have energy conversion not only at the external edge of the composite loop, but also inside the structure. The implications of these results and their relationship with the observations are discussed.

Application of Statistical Techniques to the Analysis of Solar Coronal Oscillations

In this work, the application of two different techniques to the analysis of coronal time series is investigated. The first technique, called empirical mode decomposition, was developed by Huang and coworkers and can be used to decompose a signal in its characteristic timescales, allowing, among other applications, efficient filtration of the signal. The second technique, called complex empirical orthogonal function (CEOF) analysis, is an extension of the well-known principal component analysis, to which the Hilbert transform has been added. The CEOF analysis allows identification of the dominant spatial and temporal structures in a multivariate data set and is thus ideally suited to the study of propagating and standing features that can be associated with waves or oscillations. Here we apply both methods to time series obtained from a coronal loop and obtain detailed two-dimensional information about a propagating and a standing wave with periods around 5 and 10 minutes, respectively.

The Near 160 Day Periodicity in the Photospheric Magnetic Flux

A periodicity near 154 days was discovered in the number of high-energy solar flares detected by Solar Maximum Mission (SMM) and Geosynchronous Operational Environmental Satellites (GOES) during the time interval 1980-1984 (Rieger et al.; Dennis). In this paper, we analyze the historical records of photospheric magnetic flux to show that during solar cycle 21 the periodicity appeared in the photospheric magnetic flux linked to strong magnetic fields, while it was absent during solar cycle 22. We also show that there was a time and frequency coincidence between both periodicities during solar cycle 21, which suggests the existence of a causal link between them. Taking into account that high-energy flares are triggered in regions of enhanced magnetic complexity (Kurokawa; Ishii et al.), we propose that the appearance of the periodicity in the magnetic flux materializes through the formation of new sunspots within already formed sunspot groups, setting up a suitable scenario for the occurrence of energetic flares. This scenario leads to the occurrence of periodic episodes of magnetic reconnection between old and new emergent magnetic flux, able to trigger the periodic occurrence of energetic flares recorded by SMM and GOES.

Nonlinear Instability of Kink Oscillations due to Shear Motions

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.

Magnetic Rossby Waves in the Solar Tachocline and Rieger-Type Periodicities

Apart from the eleven-year solar cycle, another periodicity around 155-160 days was discovered during solar cycle 21 in high-energy solar flares, and its presence in sunspot areas and strong magnetic flux has been also reported. This periodicity has an elusive and enigmatic character, since it usually appears only near the maxima of solar cycles, and seems to be related with a periodic emergence of strong magnetic flux at the solar surface. Therefore, it is probably connected with the tachocline, a thin layer located near the base of the solar convection zone, where a strong dynamo magnetic field is stored. We study the dynamics of Rossby waves in the tachocline in the presence of a toroidal magnetic field and latitudinal differential rotation. Our analysis shows that the magnetic Rossby waves are generally unstable and that the growth rates are sensitive to the magnetic field strength and to the latitudinal differential rotation parameters. Variation of the differential rotation and the magnetic field strength throughout the solar cycle enhance the growth rate of a particular harmonic in the upper part of the tachocline around the maximum of the solar cycle. This harmonic is symmetric with respect to the equator and has a period of 155-160 days. A rapid increase of the wave amplitude could give rise to a magnetic flux emergence leading to observed periodicities in solar activity indicators related to magnetic flux.