Transverse oscillations of two parallel coronal loops

Context. Collective oscillations of two or more coronal magnetic loops are observed very often. Aims. We study the eigenmodes of oscillations of a system consisting of two parallel magnetic loops. Methods. The linearised MHD equations for a cold plasma are solved analytically in bicylindrical coordinates using the longwavelength approximation. A dispersion equation determining the frequencies of eigenmodes is derived and solved analytically. Results. Two solutions of the dispersion relation were found. The higher frequency corresponds to the antisymmetric mode polarised in the direction parallel to the line connecting the loop centres, and the symmetric mode polarised in the perpendicular direction. Depending on the polarisation of modes corresponding to the lower frequency, the systems of two parallel loops are classified as standard and anomalous. In standard systems the lower frequency corresponds to the symmetric mode polarised in the direction parallel to the line connecting the loop centres, and the antisymmetric mode polarised in the perpendicular direction. In anomalous systems the lower frequency corresponds to the antisymmetric mode polarised in the direction parallel to the line connecting the loop centres, and the symmetric mode polarised in the perpendicular direction. The limiting case of two identical loops is studied. The results for this case are compared with recent numerical results

Line-of-sight geometrical and instrumental resolution effects on intensity perturbations by sausage modes

Diagnostics of MHD waves in the solar atmosphere is a topic which often encounters problems of interpretation, due partly to the high complexity of the solar atmospheric medium. Forward modeling can significantly guide interpretation, bridging the gap between numerical simulations and observations, and increasing the reliability of mode identification for application of MHD seismology. In this work we aim at determining the characteristics of the fast MHD sausage mode in the corona on the modulation of observable quantities such as line intensity and spectral line broadening. Effects of line-of-sight angle, and spatial, temporal and spectral resolutions are considered. We take a cylindrical tube simulating a loop in a low-{\beta} coronal environment with an optically thin background, and let it oscillate with the fast sausage mode. A parametric study is performed. Among other results, we show that regardless of the ionisation state of the plasma, the variation of spectral line broadening can be significant, even for low intensity modulation. The nature of this broadening is not thermal but is mostly turbulent. This places spectrometers in clear advantage over imaging instruments for the detection of the sausage mode. The modulation of all quantities is considerably affected by the line-of-sight angle, and especially by the spatial and temporal resolution when these are on the order of the mode's wavelength and period. This places high constraints on instrumentation.Comment: 16 pages, 20 figure

Damping of nonlinear standing kink oscillations: a numerical study

We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). We run idea, high-resolution three-dimensional (3D) magnetohydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in some cases. This questions the accuracy of seismological methods applied to observed damping profiles, based on linear theory.Comment: 10 pages, 8 figure

Coronal loop transverse oscillations excited by different driver frequencies

We analyse transverse oscillations of a coronal loop excited by continuous monoperiodic motions of the loop footpoint at different frequencies in the presence of gravity. Using the MPI-AMRVAC code, we perform three-dimensional numerical magnetohydrodynamic simulations, considering the loop as a magnetic flux tube filled in with denser, hotter, and gravitationally stratified plasma. We show the resonant response of the loop to its external excitation and analyse the development of the Kelvin-Helmholtz instability at different heights. We also study the spatial distribution of plasma heating due to transverse oscillations along the loop. The positions of the maximum heating are in total agreement with those for the intensity of the Kelvin-Helmholtz instability, and correspond to the standing wave anti-nodes in the resonant cases. The initial temperature configuration and plasma mixing effect appear to play a significant role in plasma heating by transverse footpoint motions. In particular, the development of the Kelvin-Helmholtz instability in a hotter loop results in the enhancement of the mean plasma temperature in the domain.Comment: Published in Ap

Numerical simulations of transverse oscillations in radiatively cooling coronal loops

We aim to study the influence of radiative cooling on the standing kink oscillations of a coronal loop. Using the FLASH code, we solved the 3D ideal magnetohydrodynamic equations. Our model consists of a straight, density enhanced and gravitationally stratified magnetic flux tube. We perturbed the system initially, leading to a transverse oscillation of the structure, and followed its evolution for a number of periods. A realistic radiative cooling is implemented. Results are compared to available analytical theory. We find that in the linear regime (i.e. low amplitude perturbation and slow cooling) the obtained period and damping time are in good agreement with theory. The cooling leads to an amplification of the oscillation amplitude. However, the difference between the cooling and non-cooling cases is small (around 6% after 6 oscillations). In high amplitude runs with realistic cooling, instabilities deform the loop, leading to increased damping. In this case, the difference between cooling and non-cooling is still negligible at around 12%. A set of simulations with higher density loops are also performed, to explore what happens when the cooling takes place in a very short time (tcool = 100 s). We strengthen the results of previous analytical studies that state that the amplification due to cooling is ineffective, and its influence on the oscillation characteristics is small, at least for the cases shown here. Furthermore, the presence of a relatively strong damping in the high amplitude runs even in the fast cooling case indicates that it is unlikely that cooling could alone account for the observed, flare-related undamped oscillations of coronal loops. These results may be significant in the field of coronal seismology, allowing its application to coronal loop oscillations with observed fading-out or cooling behaviour