Kink Oscillations Of Coronal Loops Research Articles

Transverse Oscillations of Coronal Loops with Slowly Changing Density

In this paper we study kink oscillations of coronal loops with the density varying along the loop and also slowly changing with time. Using the Wentzel–Kramers–Brillouin (WKB) method we obtain the adiabatic invariant that determines the time dependence of the oscillation amplitude. The obtained general results are applied to kink oscillations of cooling loops. The main conclusion of this study is that cooling causes the amplification of kink oscillations.

THE ROLE OF ACTIVE REGION LOOP GEOMETRY. II. SYMMETRY BREAKING IN THREE-DIMENSIONAL ACTIVE REGION: WHY ARE VERTICAL KINK OSCILLATIONS OBSERVED SO RARELY?

We present numerical results of simulations of kink oscillations of coronal loops in an idealized active region (AR) that is initialized as a potential dipole magnetic configuration with gravitationally stratified density. We consider loops, with density higher than the surrounding plasma, embedded into the dipolar AR. We study the excitation of kink oscillations of such loops by velocity pulses at different positions, of a given duration and amplitude. The position of the pulse varies in the parametric studies. For a central (symmetric) loop within the AR, we find that the amplitude of vertical kink oscillations is significantly amplified in comparison to horizontal kink oscillations for exciters located centrally (symmetrically) below the loop. For pulses initiated further from such a symmetric loop a combination of vertical and horizontal oscillations is excited. The scenario changes significantly when we study an inclined loop (non-symmetric within a dipole field). In this case, we do not see vertical kink oscillations of any significant amplitude being excited, while horizontal ones can be easily detected. These results indicate that the reason why vertical kink oscillations are observed so rarely is that their excitation requires a set of conditions to occur simultaneously: the exciting pulse must be located roughly below the loop apex and the loop itself must be located symmetrically within the group of loops. The new findings of the present study show the importance of not only the position of the pulse, but mainly of the location of the loop within the set of field lines having the same magnetic connectivity. We find that the slow propagating wave is excited in all the studied loops and its excitation does not depend either on the geometry of the loop or the pulse. We discuss TRACE observations of coronal loop oscillations in view of our findings and find that our results can be used for identifying the polarization of the kink mode based on the location of the loop within the set of field lines of the same connectivity and the position of the flare.

Kink and fluting modes of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section.

The Effect of Flows on Transverse Oscillations of Coronal Loops

In this paper we study kink oscillations of coronal loops in the presence of flows. Using the thin-tube approximation we derive the general governing equation for kink oscillations of a loop with the density varying along the loop in the presence of flows. This equation remains valid even when the density and flow are time dependent. The derived equation is then used to study the effect of flows on eigenfrequencies of kink oscillations of coronal loops. The implication of the obtained results on coronal seismology is discussed.

The effect of longitudinal flow on resonantly damped kink oscillations

The most promising mechanism acting towards damping the kink oscillations of coronal loops is resonant absorption. In this context most of previous studies neglected the effect of the obvious equilibrium flow along magnetic field lines. The flows are in general sub-Alfv\'enic and hence comparatively slow. Here we investigate the effect of an equilibrium flow on the resonant absorption of linear kink MHD waves in a cylindrical magnetic flux tube with the aim of determining the changes in the frequency of the forward and backward propagating waves and in the modification of the damping times due to the flow. A loop model with both the density and the longitudinal flow changing in the radial direction is considered. We use the thin tube thin boundary (TTTB) approximation in order to calculate the damping rates. The full resistive eigenvalue problem is also solved without assuming the TTTB approximation. Using the small ratio of flow and Alfv\'en speeds we derive simple analytical expressions to the damping rate. The analytical expressions are in good agreement with the resistive eigenmode calculations. Under typical coronal conditions the effect of the flow on the damped kink oscillations is small when the characteristic scale of the density layer is similar or smaller than the characteristic width of the velocity layer. However, in the opposite situation the damping rates can be significantly altered, specially for the backward propagating wave which is undamped while the forward wave is overdamped.

Resonant absorption with 2D variation of field line eigenfrequencies

Context. Resonant absorption, also known as field line resonance, can be used to describe coupling between fast and Alfven waves in non-uniform plasmas. Since the conditions for resonant absorption occur widely in astrophysics, it is applicable in many different contexts, all of which are united by their common physics. For example, resonant absorption is known to play a major role in the excitation of ultra-low frequency pulsations in the terrestrial magnetosphere and is also a leading explanation for the decay of fast kink oscillations of coronal loops. The occurrence of non-axisymmetric conditions in the magnetosphere, and observational evidence that coronal loops may possess fine transverse structure, highlight a need to consider equilibria that vary in two dimensions across the background magnetic field. Aims. We investigate the properties of resonant absorption when field line eigenfrequencies vary in two dimensions across the background magnetic field. We aim to place the theory on a firm mathematical footing and explore some of its key features. Methods. Using cold, linear, ideal MHD with a straight, uniform background magnetic field, we systematically obtain a complete analytic solution for behaviour at late times. This provides a framework from which the features of resonant absorption may be understood. The time-dependent problem is solved numerically, reproducing key features of the analytic solution. Results. Energy is deposited from a monochromatic fast wave as a phase mixing Alfven wave, in the vicinity of the resonant surface, at which the local field line eigenfrequency matches the frequency of the driver. A generalisation of the one dimensional phase mixing length to higher dimensions is suggested, and shown to successfully estimate the finest lengthscales in time-dependent simulations. The resonant Alfven wave is driven by gradients of the field aligned magnetic field perturbation, which is associated with the fast wave pressure. This leads to amplitude variations of the Alfven wave that can be used to reveal the spatial form of the fast wave.

Coronal Seismology by Means of Kink Oscillation Overtones

The detection of overtones of coronal loop kink oscillations has been an important advance in the development of coronal seismology. It has significantly increased the potential of coronal seismology and has thus initiated important theoretical and observational improvements. New detections of overtones have been made and a reduction of the error bars has been obtained. The efforts of theoreticians to extend eigenmode studies to more general coronal loop models is no longer a matter of checking the robustness of the model but now also allows for the estimation of certain equilibrium parameters. The frequencies of the detected (longitudinal) overtones are in particular sensitive to changes in the equilibrium properties along the loop, especially the density and the magnetic field expansion. Also, attempts have been made to use the limited longitudinal resolution in combination with the theoretical eigenmodes as an additional seismological tool.

The Effect of Loop Curvature on Coronal Loop Kink Oscillations

We will review analytical and numerical efforts in modelling the influence of curvature on coronal loop oscillations. We will mainly focus our attention on fast kink mode oscillations. A curved slab model will be presented, where it becomes clear that curvature introduces wave leakage into the system, because of changes in the equilibrium. The importance of leakage will be assessed through the use of a slab and cylindrical model where lateral leakage is allowed. A full analytical model for a semi-toroidal loop will be constructed for a system with no leaking waves but with an inhomogeneous layer that introduces damping due to the process of resonant absorption. The model for a semi-toroidal loop will be extended to also include leakage, and will be studied numerically. The numerical results will be compared to the analytical model.

Seismology of kink oscillations in coronal loops: Two decades of resonant damping

AbstractThe detection of rapidly damped transverse oscillations in coronal loops by Aschwanden et al. (1999) and Nakariakov et al. (1999) gave a strong impetus to the study of MHD waves and their damping. The common interpretation of the observations of these oscillations is based on kink modes. This paper reviews how the observed period and damping time can be reproduced by MHD wave theory when non-uniform equilibrium models are considered that have a transversal variation of the local Alfven velocity. The key point here is that resonant absorption cannot be avoided and occurs as natural damping mechanism for kink waves in non-uniform equilibrium models. The present paper starts with work by Hollweg & Yang (1988) and discusses subsequent developments in theory and their applications to seismology of coronal loops. It addresses the consistent use of observations of periods and damping times as seismological tools within the framework of resonant absorption. It shows that within the framework of resonant absorption infinitely many equilibrium models can reproduce the observed values of periods and damping times.

Damping of vertical coronal loop kink oscillations through wave tunneling

The decay rate of vertical kink waves in a curved flux tube is modeled numerically. The full MHD equations are solved for a curved equilibrium flux tube in an arcade geometry and the decay of ψ, the integral over the flux tube of the modulus of the velocity perpendicular to the local magnetic field, is measured. These simulations are 2D and are thus restricted to kink oscillations in the loop plane. The decay rate is found to increase with increasing wavelength, increasing β and decreasing density contrast ratio. The wave tunneling effect is shown to be a possible mechanism for the high decay rate of the recent observed kink oscillation reported by Wang & Solanki (2004).

Coronal Leaky Tube Waves and Oscillations Observed with Trace

Leaky tube waves are examined in the context of kink oscillations in coronal loops, observed in recent years using TRACE. It is pointed out that the standard (non-leaky) principal kink mode has a leaky bifurcated counterpart with decay time τl≈4π−4(L/R)2P, where R and L are the loop radius and length, and P is the oscillation period. This is somewhat too long to explain the observed decays, except for very short or thick loops, but may be implicated in the initial excitation. Higher harmonics decay much more rapidly. The external solution takes the form of a wave running nearly parallel to the tube, but with a small outward component. In addition, a number of other leaky modes are described which decay on timescales of seconds, τl=Rae/a2, where a and ae are the loop and external Alfven speeds respectively, and which can be identified as being almost radially propagating fast magnetoacoustic waves. These are outside the currently observable range, but are likely to be important energetically.