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Register a new userTransverse kink oscillations of expanding coronal loops
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We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations. Due to the uncertainty of the loops shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies. Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loops length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage.
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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.
Evidence of flare induced, large-amplitude, decay-less transverse oscillations is presented. A system of multi-thermal coronal loops as observed with the Atmospheric Imaging Assembly (AIA), exhibit decay-less transverse oscillations after a flare erupts nearby one of the loop footpoints. Measured oscillation periods lie between 4.2 min and 6.9 min wherein the displacement amplitudes range from 0.17 Mm to 1.16 Mm. A motion-magnification technique is employed to detect the pre-flare decay-less oscillations. These oscillations have similar periods (between 3.7 min and 5.0 min) like the previous ones but their amplitudes (0.04 Mm to 0.12 Mm) are found to be significantly smaller. No phase difference is found among oscillating threads of a loop when observed through a particular AIA channel or when their multi-channel signatures are compared. These features suggest that the occurrence of a flare in this case neither changed the nature of these oscillations (decaying vs decay-less) nor the oscillation periods. The only effect the flare has is to increase the oscillation amplitudes.
The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and interpreted in terms of MHD kink modes of cylindrical plasma waveguides. Recent observational analysis has revealed the so-called decay-less small-amplitude oscillations, with a multi-harmonic structure being detected. Several models have been proposed to explain them. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous monoperiodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we consider transverse loop oscillations driven by random motions of footpoints. The footpoint motions are modelled by broad-band coloured noise. We have found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and generation of multiple harmonics detected recently. We propose the mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.
Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant alpha-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actual period is increasingly smaller than the one estimated by WKB theory. Translated through coronal seismology, increasing sigmoidity results in magnetic field estimates which are increasingly shifting towards higher values, and even surpassing the average value for the highest alpha value considered. Nevertheless, the estimated range of the coronal magnetic field value lies within the mimimal/maximal limits, proving the robustness coronal seismology. We propose that the discrepancy in the estimations of the absolute value of the force-free magnetic field could be exploited seismologically to determine the free energy of coronal loops, if averages of the internal magnetic field and density can be reliably estimated by other methods.
We simulate transverse oscillations in radiatively cooling coronal loops and forward-model their spectroscopic and imaging signatures, paying attention to the influence of background emission. The transverse oscillations are driven at one footpoint by a periodic velocity driver. A standing kink wave is subsequently formed and the loop cross-section is deformed due to the Kelvin-Helmholtz instability, resulting in energy dissipation and heating at small scales. Besides the transverse motions, a long-period longitudinal flow is also generated due to the ponderomotive force induced slow wave. We then transform the simulated straight loop to a semi-torus loop and forward-model their spectrometer and imaging emissions, mimicking observations of Hinode/EIS and SDO/AIA. We find that the oscillation amplitudes of the intensity are different at different slit positions, but are roughly the same in different spectral lines or channels. X-t diagrams of both the Doppler velocity and the Doppler width show periodic signals. We also find that the background emission dramatically decreases the Doppler velocity, making the estimated kinetic energy two orders of magnitude smaller than the real value. Our results show that background subtraction can help recover the real oscillation velocity. These results are helpful for further understanding transverse oscillations in coronal loops and their observational signatures. However, they cast doubt on the spectroscopically estimated energy content of transverse waves using the Doppler velocity.
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