T. Van Doorsselaere

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.

Detection of waves in the solar corona : kink or Alfven?

Recently, the omnipresence of waves has been discovered in the corona using the CoMP instrument. We demonstrate that the observational findings can be explained in terms of guided kink magnetoacoustic modes. The interpretation of the observations in terms of Alfven waves is shown to be inconsistent with MHD wave theory. The implications of the interpretation in terms of kink waves are discussed.

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%.

Coronal loop seismology using multiple transverse loop oscillation harmonics

Context. TRACE observations (23/11/1998 06:35:57−06:48:43 UT) in the 171 A bandpass of an active region are studied. Coronal loop oscillations are observed after a violent disruption of the equilibrium. Aims. The oscillation properties are studied to give seismological estimates of physical quantities, such as the density scale height. Methods. A loop segment is traced during the oscillation, and the resulting time series is analysed for periodicities. Results. In the loop segment displacement, two periods are found: 435.6 ± 4. 5sa nd 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. Because a loop segment is traced, the amplitude dependence along the loop is found for each of these oscillations. The obtained spatial information is used as a seismological tool to give details about the geometry of the observed loop.

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.

Coronal magnetic field measurement using loop oscillations observed by Hinode/EIS

We report the first spectroscopic detection of a kink MHD oscillation of a solar coronal structure by the Extreme-Ultraviolet Imaging Spectrometer (EIS) on the Japanese Hinode satellite. The detected oscillation has an amplitude of 1 kms−1 in the Doppler shift of the FeXII 195 A spectral line (1.3 MK), and a period of 296 s. The unique combination of EIS’s spectroscopic and imaging abilities enables us to measure simultaneously the mass density and length of the oscillating loop. This enables us to measure directly the magnitude of the local magnetic field, the fundamental coronal plasma parameter, as 39 ± 8 G, with unprecedented accuracy. This proof of concept makes EIS an exclusive instrument for the full scale implementation of the MHD coronal seismological technique.

Seismology of a large solar coronal loop from EUVI/STEREO observations of its transverse oscillation

The first analysis of a transverse loop oscillation observed by both Solar TErrestrial RElations Observatories (STEREO) spacecraft is presented, for an event on the 2007 June 27 as seen by the Extreme Ultraviolet Imager (EUVI). The three-dimensional loop geometry is determined using a three-dimensional reconstruction with a semicircular loop model, which allows for an accurate measurement of the loop length. The plane of wave polarization is found from comparison with a simulated loop model and shows that the oscillation is a fundamental horizontally polarized fast magnetoacoustic kink mode. The oscillation is characterized using an automated method and the results from both spacecraft are found to match closely. The oscillation period is 630 {+-} 30 s and the damping time is 1000 {+-} 300 s. Also, clear intensity variations associated with the transverse loop oscillations are reported for the first time. They are shown to be caused by the effect of line-of-sight integration. The Alfven speed and coronal magnetic field derived using coronal seismology are discussed. This study shows that EUVI/STEREO observations achieve an adequate accuracy for studying long-period, large-amplitude transverse loop oscillations.

Seismological demonstration of perpendicular density structuring in the solar corona

The peculiarities of the propagating transverse waves observed in the solar corona with the Coronal Multi-channel Polarimeter (CoMP) indicate the existence of fine field structuring in the coronal density. We present results of numerical simulations studying the evolution of a localised transverse magneto-hydrodynamic wave in a uniform magnetic field. We consider two initial low plasma-beta equilibria: one with a homogeneous density, and one with a field-aligned dense structure (such as a loop or a plume). The perpendicular localisation of the wave strongly determines the angular distribution of the energy propagation. If the perpendicular scale of the wave is significantly smaller than the parallel scale (e.g. wavelength), as established by CoMP, the wave develops as an oblique fast magneto-acoustic wave. In an unstructured medium, the energy of such a wave is transferred mainly across the magnetic field. However, it is possible to channel the energy of the transverse wave along the magnetic field in the presence of a field-aligned density enhancement. We conclude that the CoMP results provide an independent seismological proof that the corona is structured in density in the perpendicular direction.

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.