Jesse Andries

Coronal loop oscillations - An interpretation in terms of resonant absorption of quasi-mode kink oscillations

Damped quasi-mode kink oscillations in cylindrical flux tubes are capable of explaining the observed rapid damping of the coronal loop oscillations when the ratio of the inhomogeneity length scale to the radius of the loop is allowed to vary from loop to loop, without the need to invoke anomalously low Reynolds numbers. The theoretical expressions for the decay time by Hollweg & Yang ([CITE]) and Ruderman & Roberts ([CITE]) are used to estimate the ratio of the length scale of inhomogeneity compared to the loop radius for a collection of loop oscillations.

Determination of the Coronal Density Stratification from the Observation of Harmonic Coronal Loop Oscillations

The recent detection of multiple harmonic standing transverse oscillations in coronal loops by Verwichte et al. is of special importance, as it allows one to obtain information on the longitudinal density variation in loops. Verwichte et al. detected the simultaneous presence of both the fundamental and the first-overtone mode in two coronal loops. Here we point out that the ratio of the period of the fundamental mode to the period of the overtone mode differs from 2 in loops with longitudinal density stratification. Conversely, the difference between this ratio and 2 can be used as a seismological tool to obtain information about the density scale height in loops.

Coronal loop oscillations Calculation of resonantly damped MHD quasi-mode kink oscillations of longitudinally stratified loops

The observed coronal loop oscillations and their damping are often theoretically described by the use of a very simple coronal loop model, viz. a straight, longitudinally invariant, axi-symmetric, and pressureless flux tube with a different density inside and outside of the loop. In this paper we generalize the model by including longitudinal density stratification and we examine how the longitudinal density stratification alters the linear eigenmodes of the system, their oscillation frequencies, and the damping rates by resonant absorption.

Damping of Coronal Loop Oscillations: Calculation of Resonantly Damped Kink Oscillations of One-dimensional Nonuniform Loops

The analytic study of coronal loop oscillations in equilibrium states with thin nonuniform boundary layers is extended by a numerical investigation for one-dimensional nonuniform equilibrium states. The frequency and the damping time of the ideal kink quasi mode are calculated in fully resistive MHD. In this numerical investigation there is no need to adopt the assumption of a thin nonuniform boundary layer, which is essential for analytic theory. An important realization is that analytical expressions for the damping rate that are equivalent for thin nonuniform layers give results differing by a factor of 2 when they are used for thick nonuniform layers. Analytical theory for thin nonuniform layers does not allow us to discriminate between these analytical expressions. The dependence of the complex frequency of the kink mode on the width of the nonuniform layer, on the length of the loop, and on the density contrast between the internal and the external region is studied and is compared with analytical theory, which is valid only for thin boundaries. Our numerical results enable us to show that there exists an analytical expression for thin nonuniform layers that might be used as a qualitative tool for extrapolation into the regime of thick nonuniform layers. However, when the width of the nonuniform layer is varied, the differences between our numerical results and the results obtained with the version of the analytical approximation that can be extended into the regime of thick nonuniform layers are still as large as 25%.

MHD seismology of coronal loops using the period and damping of quasi-mode kink oscillations

Aims. We combine the magnetohydrodynamic (MHD) theory of resonantly damped quasi-mode kink oscillations with observational estimates of the period and damping of transverse coronal loop oscillations to extract information on physical parameters in oscillating loops. Methods. A numerical study of the quasi-mode period and damping, in one-dimensional fully non-uniform flux tubes, is used to obtain equilibrium models that reproduce the observed periods and damping rates. This scheme is applied to 11 loop oscillation events. Results. When only the damping rate is used, the valid equilibrium models form a one-dimensional solution curve in the two-dimensional parameter space (density contrast, transverse inhomogeneity length-scale). Lower limits to the transverse inhomogeneity are obtained in the limit of high contrast loops. When both the period and the damping rate are used, the equilibrium Alfven speed (or Alfven travel time) comes into play. The valid equilibrium models then form a one-dimensional solution curve in the three-dimensional parameter space (density contrast, transverse inhomogeneity length-scale, Alfven speed or Alfven travel time). The projection of these solutions onto the Alfven speed axis is found to be constrained to a rather limited interval. Upper limits to the internal Alfven speed are derived for 9 of the 11 analysed events.

The effect of curvature on quasi-modes in coronal loops

This paper studies quasi-mode oscillations in models of coronal loops that include longitudinal curvature. Using a toroidal coordinate system to incorporate curvature in a basic coronal loop model, the linearized ideal MHD equations are solved for the plasma-β = 0. As a result of the curvature, quasi-modes with different poloidal wave numbers are coupled resulting in modifications of the frequencies. However, for small curvature, only the coupling of quasi-modes with a neighbouring poloidal wave number remains in first order. In addition, the quasi-mode frequencies are unchanged up to first order in the curvature. The imaginary part of the frequency, however, does change in first order, and quasi-modes are slightly more damped in realistically curved coronal loop configurations.

Damping of magnetohydrodynamic waves by resonant absorption in the solar atmosphere

In the last decade we have been overwhelmed by an avalanche of discoveries of magnetohydrodynamic (MHD) waves by the Solar and Heliospheric Observatory and Transition Region and Coronal Explorer observatories. Both standing and propagating versions of fast magnetoacoustic and slow magnetoacoustic MHD waves have been detected. Information on the damping times and damping distances of these waves is less detailed and less accurate than that on periods and amplitudes. Nevertheless, observations show the damping times and damping lengths are often short. Also, different types of MHD waves in different types of magnetic structures likely require different damping mechanisms. The phenomenon of fast damping is well documented for the standing fast magnetosonic kink waves in coronal loops. This paper concentrates on standing fast magnetosonic waves. It reports on results on periods and damping times due to resonant absorption in one-dimensional and two-dimensional models of coronal loops. Special attention is given to multiple modes.

SURFACE ALFVEN WAVES IN SOLAR FLUX TUBES

Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. Alfven waves and magneto-sonic waves are particular classes of MHD waves. These wave modes are clearly different and have pure properties in uniform plasmas of infinite extent only. Due to plasma non-uniformity, MHD waves have mixed properties and cannot be classified as pure Alfven or magneto-sonic waves. However, vorticity is a quantity unequivocally related to Alfven waves as compression is for magneto-sonic waves. Here, we investigate MHD waves superimposed on a one-dimensional non-uniform straight cylinder with constant magnetic field. For a piecewise constant density profile, we find that the fundamental radial modes of the non-axisymmetric waves have the same properties as surface Alfven waves at a true discontinuity in density. Contrary to the classic Alfven waves in a uniform plasma of infinite extent, vorticity is zero everywhere except at the cylinder boundary. If the discontinuity in density is replaced with a continuous variation of density, vorticity is spread out over the whole interval with non-uniform density. The fundamental radial modes of the non-axisymmetric waves do not need compression to exist unlike the radial overtones. In thin magnetic cylinders, the fundamental radial modes of the non-axisymmetric waves with phase velocities between the internal and the external Alfven velocities can be considered as surface Alfven waves. On the contrary, the radial overtones can be related to fast-like magneto-sonic modes.

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.

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.