R. Oliver

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.

FAST MAGNETOHYDRODYNAMIC OSCILLATIONS IN CYLINDRICAL PROMINENCE FIBRILS

Some observations suggest that quiescent solar prominences can be considered as composed by small-scale loops, or fibrils, which are stacked one after another in both the vertical and horizontal directions. In a previous work we studied, in Cartesian geometry, the propagation of fast MHD waves in a two-dimensional magnetostatic model representing one of these fibrils. Since this is a crude model to represent a real fibril, in this paper we use a more realistic model based on a cylindrically symmetric flux tube and study the propagation of fast MHD waves in this structure. A new array of modes of oscillation, together with their periods and spatial properties, is described, showing several important differences with respect to the properties of modes in Cartesian geometry. Among other conclusions, our results show that all sausage modes (m = 0) possess a cutoff frequency, while the fundamental kink and fluting modes (m > 0) do not show such a cutoff. In addition, the frequency of these modes is independent of the azimuthal wavenumber (m) and of the fibril thickness for a wide range of values of this parameter, which is an important fact for prominence seismology. Moreover, the spatial structure of the modes below the cutoff frequency is such that in this geometry perturbations are confined in the dense part of the fibril, the leakage of energy toward the coronal medium being very small, which may prevent the excitation of neighboring fibrils. Finally, diagnostic diagrams displaying the oscillatory period in terms of some equilibrium parameters are provided in order to allow for a comparison between our theoretical results and those coming from observations.

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.

The periodic behaviour of the North-South asymmetry of sunspot areas revisited

Up to now, the periodic behaviour of the N-S asymmetry of solar activity has been analyzed by applying the power spectrum analysis to the time series generated from a normalized definition of the asymmetry. Using sunspot areas and the properties of the discrete Fourier transform, we show that the use of the normalized time series leads to misleading results, and that the correct asymmetry time series to be used is generated from the difference between the values of solar activity indicators in the Northern and Southern solar hemispheres. However, in this case the found significant periodicities correspond to periodicities already present in the hemispheric sunspot areas time series, not providing with any interesting information about the asymmetric behaviour of the solar activity. Of course, our conclusions are extensive to all the studies of the periodic behaviour of the N-S asymmetry of solar activity time series computed by means of the normalized definition of the asymmetry, and independent of the considered solar activity feature.

Damping of oscillations by ion-neutral collisions in a prominence plasma

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.

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.

Time damping of linear non-adiabatic magnetohydrodynamic waves in an unbounded plasma with solar coronal properties

In this paper, we study the time damping of magnetoacoustic waves when the adiabaticity assumption is removed by means of an energy equation which includes optically thin radiative losses, thermal conduction and heating. For the sake of simplicity, this study has been done for a homogeneous, isothermal and unbounded medium permeated by a uniform magnetic field, with physical properties akin to those of the corona, the prominence-corona transition region (PCTR) and prominences. In some PCTR regimes and in the coronal regime wave instabilities appear, which prevents the computation of the damping time and the damping per period for part of the wavenumber interval considered. Furthermore, except for one of the PCTR regimes, in the rest of the regimes the apparition of those instabilities depends on the heating mechanism considered. Also, for the same heating mechanism, the behaviour of the damping time for the different considered regimes changes significantly when going from very small to very large wavenumbers and, in all the regimes, it becomes almost constant for very large wavenumbers.