Coronal Loop Oscillations Research Articles

Fast magnetohydrodynamic oscillations of a coronal loop embedded in a potential coronal arcade

Observations indicate variable widths exhibited by fan coronal loops and flare loops that tend to widen towards the apex. Short-period, quasi-periodic pulsations in solar flares are often interpreted in terms of the fast-sausage oscillations of flare loops and the collective vertical vibrations of arcade loops are attributed with the vertical kink mode. Both phenomena are used as a seismological tool to estimate the physical parameters in the corona. We performed an analytical study of fast sausage and kink oscillations in coronal loops, given the effects of loop curvature, expansion, and Alfv \'e n speed variation. We modelled a coronal loop as a dense expanding curved magnetic slab embedded within a potential coronal arcade, using a zero-beta plasma limit. We obtained the dispersion relation that governs fast waves in the model and studied it both numerically and analytically. The effects of loop expansion and variable Alfv \'e n speed reduce the cut-off frequency and increase the cut-off wavenumbers for fast sausage and kink waves. Moreover, the principal vertical kink mode has a cut-off and strongly attenuates in the leaky regime. The frequency increase is found to be minor for the global sausage mode both in the trapped and leaky regimes, with a frequency shift within a few percent. We found that in our model, where the Alfv \'e n speed increases from the footpoints to the loop top, the spatial profile of the longitudinal fundamental is broadened and the antinodes of the first overtone are shifted towards the footpoints. Using the classical expression for the cut-off wavenumber of the global sausage mode in a straight waveguide results in an underestimation of the density contrast constraint in flare loops. Instead, the suggested formula accounting for variations in loop widths provides more accurate results. The frequency of the global sausage mode can be correctly determined with the straight slab model.

Effects of coronal rain on decayless kink oscillations of coronal loops

Decayless kink oscillations are ubiquitously observed in active region coronal loops with an almost constant amplitude for several cycles. Decayless kink oscillations of coronal loops triggered by coronal rain have been analyzed, but the impact of coronal rain formation in an already oscillating loop is unclear. As kink oscillations can help diagnose the local plasma conditions, it is important to understand how these are affected by coronal rain phenomena. In this study, we present the analysis of an event of coronal rain that occurred on 25 April 2014 and was simultaneously observed by Slit-Jaw Imager (SJI) on board Interface Region Imaging Spectrograph (IRIS) and Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO). We investigated the oscillation properties of the coronal loop in AIA images before and after the appearance of coronal rain as observed by SJI. We find signatures of decayless oscillations before and after coronal rain at similar positions to those found during coronal rain. The individual cases show a greater amplitude and period during coronal rain. The mean period is increased by 1.3 times during coronal rain, while the average amplitude is increased by 2 times during rain, in agreement with the expected density increase from coronal rain. The existence of the oscillations in the same loop at the time of no coronal rain indicates the presence of a footpoint driver. The properties of the observed oscillations during coronal rain can result from the combined contribution of coronal rain and a footpoint driver. The oscillation amplitude associated with coronal rain is approximated to be 0.14 Mm. The properties of decayless oscillations are considerably affected by coronal rain, and without prior knowledge of coronal rain in the loop, a significant discrepancy can arise from coronal seismology with respect to the true values.

Transverse Oscillations and Kelvin–Helmholtz Instability in Curved Arcade Loops with Siphon Flows

The effect of plasma flow in curved arcade loops on transverse waves and oscillations is examined analytically. The model under study is a semicircular magnetic slab with finite transverse extensions and a mass flow inside, in the zero-β plasma approximation. It is found that in the quasi-perpendicular propagation limit, the model supports two fast surface modes: one with higher (FSW+) and another with lower (FSW−) frequency. For a weak flow, the frequency of the FSW+ (FSW−) increases (decreases) as the flow speed grows in both propagating and quasi-standing wave regimes. We show that the FSW+ and FSW− are subjected to the Kelvin–Helmholtz (KH) instability, and the threshold flow is greater (less than) the internal Alfvén speed for the FSW+ (FSW−). The presence of plasma flow results in modifying the period ratio P 1/2P 2 of the fundamental harmonic to the first overtone with P 1/2P 2 less (more) than 1 for the FSW+ (FSW−), and this effect degenerates in the straight waveguide limit. The sub-Alfvénic flow can prohibit resonant absorption of kink modes when the frequencies of the FSW+ and FSW− become out of the Alfvén continuum. It is also shown that in the static case and for a weak flow case, the FSW+ (FSW−) is interpreted as a vertically (horizontally) polarized kink mode, while for moderate flow, both modes have oblique polarization. We apply the developed theory to interpret the observational cases of kink oscillations in coronal loops with signatures of a siphon flow and the onset of KH instability induced by the blowout jet along a loop-shaped magnetic structure.

Transition from decaying to decayless kink oscillations of solar coronal loops

ABSTRACT The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e. the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterized by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

Analytical Study of Damped Standing Longitudinal MHD Waves in Flowing Coronal Loops: The Effect of Thermal Conduction

The longitudinal magnetohydrodynamic (MHD) oscillations of coronal loops have been investigated in dissipative flowing loops. Thermal conduction has been considered as the damping mechanism of the wave. We aim to construct the damped longitudinal waves by superposing two propagating waves that propagate in opposite directions. The two propagating components must have the same oscillation frequencies and damping rates, which has been described impossible by some authors, but we have used a technique to overcome this difficulty. The equations of motion are combined to obtain a differential equation for the velocity perturbation. Using the weak damping condition, the perturbation method is used to solve the dispersion relation. In the leading order approximation, the oscillation frequency of the standing waves is determined. In the first-order approximation, we let both the oscillation frequency and wavelength of the propagating waves be perturbed due to the presence of thermal conduction, which enables us to determine the damping rate of the standing waves. Our results show that the plasma flow is an essential parameter in determining the effectiveness of the damping mechanism. Also, the exact solutions of the dispersion relation have been determined without using weak damping assumption. Interestingly the two solutions are the same. Introducing plasma flow to the coronal loop causes the period ratio of the fundamental mode to the first overtone to decrease more.

Statistical investigation of decayless oscillations in small-scale coronal loops observed by Solar Orbiter/EUI

Decayless kink oscillations are omnipresent in the solar atmosphere, and they are a viable candidate for coronal heating. Although there have been extensive studies of decayless oscillations in coronal loops with lengths of a few hundred megameters, the properties of these oscillations in small-scale (∼10 mm) loops are yet to be explored. In this study, we present the properties of decayless oscillations in small loops embedded in the quiet corona and coronal holes. We use high-resolution observations from the Extreme Ultraviolet Imager on board Solar Orbiter with pixel scales of 210 km and a cadence of 5 s or better. We analysed 42 oscillations in coronal loops with loop lengths varying between 3 to 23 mm. The average displacement amplitude is found to be 134 km. The oscillations period has a range of 28 to 272 s, and the velocity amplitudes range from 2.1 to 16.4 km s−1. The variation in the loop length with the period does not indicate a significant correlation. The wave mode of these waves is uncertain, and standing waves are one possibility. Our results for the coronal seismology and energy flux estimates were obtained considering standing modes. The observed kink speeds are lower than those observed in active region coronal loops. We obtain an average magnetic field value of 2.1 G. We estimated the energy flux with a broad range of 0.6–313 W m−2. Moreover, we note that short-period decayless oscillations are not prevalent in the quiet Sun and coronal holes. Our study suggests that decayless oscillations in small-scale coronal loops are unlikely to provide enough energy to heat the quiet Sun and accelerate solar wind in coronal holes.

Nonlinear Wave Damping by Kelvin–Helmholtz Instability-induced Turbulence

Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured medium, for example, transverse oscillations of coronal loops. Linear theory has provided many insights into the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona from observed wave periods and damping times. However, simulations show that nonlinear kink waves can host the Kelvin–Helmholtz instability (KHI), which subsequently creates turbulence in the loop, dynamics that are beyond linear models. In this paper we investigate the evolution of KHI-induced turbulence on the surface of a flux tube where a nonlinear fundamental kink mode has been excited. We control our numerical experiment so that we induce the KHI without exciting resonant absorption. We find two stages in the KHI turbulence dynamics. In the first stage, we show that the classic model of a KHI turbulent layer growing at ∝t is applicable. We adapt this model to make accurate predictions of the damping of the oscillation and turbulent heating as a consequence of the KHI dynamics. In the second stage, the now dominant turbulent motions are undergoing decay. We find that the classic model of energy decay proportional to t −2 approximately holds and provides an accurate prediction of the heating in this phase. Our results show that we can develop simple models for the turbulent evolution of a nonlinear kink wave, but the damping profiles produced are distinct from those of linear theory that are commonly used to confront theory and observations.

Effect of magnetically dependent heating on the behaviour of magnetoacoustic waves in coronal plasma with thermal misbalance

ABSTRACT The magnetic nature of coronal heating has been actively investigated within the framework of theoretical models and statistical analysis of observational data for decades. At present, a rather wide range of possible mechanisms has been proposed in the literature that requires additional verification. In this paper, we investigate the possibility of analysing the magnetic nature of coronal heating by means of magnetoacoustic (MA) waves propagating in coronal structures. To address this issue, we perform the analysis of fast and slow waves using a magnetic slab geometry. Applying the assumption of strong magnetic structuring, we derive the dispersion relation, which allows us to study the properties of MA waves. To analyse the dependence of phase velocity and wave decrement/increment on wavenumber, we numerically solved the obtained equations using the parameters corresponding to ‘warm’ coronal loop. It is shown that oscillations on the fundamental harmonic in a plasma with a weak magnetic field, where the effect of phase velocity dispersion is most pronounced, are best suited for diagnostics of magnetic heating using slow MA waves. In turn, the geometry remains the primary source for fast MA wave dispersion. Magnetic heating can either suppress or increase the damping of fast and slow MA waves. Moreover, the amplification of fast MA waves accompanied by damping of slow MA waves can be achieved. This issue is of interest in the context of the excitation of the decayless kink oscillations in the solar coronal loops.

Decayless oscillations in 3D coronal loops excited by a power-law driver

Aims. We studied the manifestation of decayless oscillations in 3D simulations of coronal loops, driven by random motions. Methods. Using the PLUTO code, we ran magnetohydrodynamic (MHD) simulations of a straight gravitationally stratified flux tube, with its footpoints embedded in chromospheric plasma. We consider transverse waves drivers with a horizontally polarised red noise power-law spectrum. Results. Our broadband drivers lead to the excitation of standing waves with frequencies equal to the fundamental standing kink mode and its harmonics. These standing kink oscillations have non-decaying amplitudes, and spectra that depend on the characteristics of the loops, with the latter amplifying the resonant frequencies from the drivers. We thus report for the first time in 3D simulations the manifestation of decayless oscillations from broadband drivers. The spatial and temporal evolution of our oscillation spectra reveals the manifestation of a half harmonic, which exhibits half the frequency of the identified fundamental mode with a similar spatial profile. Our results suggest that this mode is related to the presence of the transition region in our model and could be interpreted as being the equivalent to the fundamental mode of standing sound waves driven on pipes closed at one end. Conclusions. The potential existence of this half harmonic has important implications for coronal seismology, since misinterpreting it for the fundamental mode of the system can lead to false estimations of the average kink speed profile along oscillating loops. Finally, its detection could potentially give us a tool for distinguishing between different excitation and driving mechanisms of decayless oscillations in observations.

Decayless low-amplitude transverse oscillations in short coronal loops as manifestations of driven slow modes

ABSTRACT A recent theoretical study of slow magnetoacoustic oscillations in a curved magnetic slab shows that the principal slow mode causes both dominant longitudinal motions and radial (transverse) kink-like motions of a slab. This modification of wave properties occurs due to the violation of the symmetry of wave motions with respect to the waveguide axis and the slow to fast wave interaction in curved magnetic configurations. In this work, we carry out a comprehensive investigation of the principal slow mode depending on the model parameters. It is shown that the dominance of longitudinal motions in the principal slow mode decreases as both the internal plasma-β and slab aspect ratio increase. The results are used to explain the observed small amplitude decayless transverse oscillations in short coronal loops. In particular, these phenomena are interpreted as direct manifestation of slow mode oscillations in curved coronal loops excited at the footpoints by compressible oscillations of the underlying atmospheric layers. Numerical calculations have shown that the observed velocity range of V = 0.6–5 km s−1 corresponds to radial velocity amplitudes in the principal slow mode, provided that the plasma-β inside the short loops is in the range of βi= 0.3–0.5 and the loop aspect ratio 0.15 ≤ a/R ≤ 0.25. These parameters appear to be typical for low-lying small coronal loops extending from the transition region to the lower corona.

Measuring local physical parameters in coronal loops with spatial seismology

Context. The method of spatial seismology can be applied to the amplitude profile of transverse coronal loop oscillations to constrain the distributions of physical parameters, such as the loop density, magnitude of the magnetic field, and so on. Aims. We intend to develop and apply a practical spatial seismology technique to detect physical parameters of plasma and validate its effectiveness by comparing it with other methods. Methods. A spatial seismology inversion was conducted by numerically optimizing a parametric dynamic model of the loop’s density stratification and magnetic field variation to best fit the measured amplitude profile of the loop. Results. The spatial seismology inversion technique developed here was applied to a transverse coronal loop oscillation that occurred on 2013 April 11, whose oscillation amplitude profile of both the fundamental mode and first overtone was reported in previous work. The consistency between the time domain analysis and spatial seismology has been verified. Meanwhile, we accounted for the asymmetric profile of the fundamental mode by forward modeling and we derived the magnetic field distribution by inverse modeling, which is coincident with that of the extrapolated one. In addition, spatial seismology inversion was applied to the transverse oscillation event on 2022 March 30 to obtain the distribution of the loop’s density and magnetic field, which are compared with the results derived from the differential emission measure (DEM) diagnostics and the direct potential field extrapolation. Conclusions. Spatial seismology inversion can be used as an effective method to independently measure various physical parameters, for example the density and magnetic field of coronal loops, which are consistent with the results obtained by DEM diagnostics and potential field extrapolation.

Modeling of Transverse Oscillations Driven by p-modes in Short Coronal Loops

Recent observations have revealed two types of decayless transverse oscillations in short coronal loops: one with short periods scaling with loop lengths, and the other with longer periods that exhibit a peak at around 5 minutes in the period distribution. To understand such a difference in period, we work in the framework of ideal MHD and model a short coronal loop embedded in an atmosphere with density stratification from the chromosphere to the corona. An inclined p-mode-like driver with a period of 5 minutes is launched at one loop footpoint. It is discovered that two types of decayless transverse oscillations can be excited in the loop. We interpret the 5 minutes periodicity as being directly driven by the footpoint driver, while the others, with periods of several tens of seconds, are regarded as kink eigenmodes of different harmonics. Therefore, our simulation shows that both types of decayless oscillations found in observations can be excited by p-modes in one short coronal loop. This study extends our understanding of ubiquitous decayless transverse oscillations in the corona. Furthermore, it suggests that p-modes could be an important energy source for coronal heating by driving decayless transverse oscillations.

Comparison of damping models for kink oscillations of coronal loops

ABSTRACT Kink oscillations of solar coronal loops are of intense interest due to their potential for diagnosing plasma parameters in the corona. The accurate measurement of the kink oscillation damping time is crucial for precise seismological diagnostics, such as the transverse density profile, and for the determination of the damping mechanism. Previous studies of large-amplitude rapidly decaying kink oscillations have shown that both an exponential damping model and a generalized model (consisting of Gaussian and exponential damping patterns) fit observed damping profiles sufficiently well. However, it has recently been shown theoretically that the transition from the decaying regime to the decayless regime could be characterized by a superexponential damping model. In this work, we reanalyse a sample of decaying kink oscillation events, and utilize the Markov chain Monte Carlo Bayesian approach to compare the exponential, Gaussian–exponential, and superexponential damping models. It is found that in 7 out of 10 analysed oscillations, the preferential damping model is the superexponential one. In two events, the preferential damping is exponential, and in one it is Gaussian–exponential. This finding indicates the plausibility of the superexponential damping model. The possibility of a non-exponential damping pattern needs to be taken into account in the analysis of a larger number of events, especially in the estimation of the damping time and its associated empirical scalings with the oscillation period and amplitude, and in seismological inversions.

30-min decayless kink oscillations in a very long bundle of solar coronal plasma loops

The energy balance in the corona of the Sun is the key to the long-standing coronal heating dilemma, which could be potentially revealed by observational studies of decayless kink oscillations of coronal plasma loops. A bundle of very long off-limb coronal loops with the length of 736pm 80 Mm and a lifetime of about 2 days are found to exhibit decayless kink oscillations. The oscillations are observed for several hours. The oscillation amplitude is measured at 0.3–0.5 Mm, and the period at 28–33 min. The existence of 30-min periodicity of decayless kink oscillations indicates that the mechanism compensating the wave damping is still valid in such a massive plasma structure. It provides important evidence for the non-resonant origin of decayless kink oscillations with 2–6 min periods, i.e., the lack of their link with the leakage of photospheric and chromospheric oscillations into the corona and the likely role of the broadband energy sources. Magnetohydrodynamic seismology based on the reported detection of the kink oscillation, with the assistance of the differential emission measure analysis and a background coronal model provides us with a comprehensive set of plasma and magnetic field diagnostics, which is of interest as input parameters of space weather models.

Damping of coronal oscillations in self-consistent 3D radiative magnetohydrodynamics simulations of the solar atmosphere

Context. Oscillations are abundant in the solar corona. Coronal loop oscillations are typically studied using highly idealised models of magnetic flux tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of a realistic magnetic field topology and the density structuring. Aims. We analyse the damping of coronal oscillations using a self-consistent 3D radiation-magnetohydrodynamics simulation of the solar atmosphere spanning from the convection zone into the corona, the associated oscillation dissipation and heating, and finally, the physical processes that cause the damping and dissipation. The simulated corona that forms in this model does not depend on any prior assumptions about the shape of the coronal loops. Methods. We analysed the evolution of a bundle of magnetic loops by tracing the magnetic field. Results. We find that the bundle of magnetic loops shows damped transverse oscillations in response to perturbations in two separate instances, with oscillation periods of 177 s and 191 s, velocity amplitudes of 10 km s−1 and 16 km s−1, and damping times of 176 s and 198 s. The coronal oscillations lead to the development of velocity shear in the simulated corona, which results in the formation of vortices seen in the velocity field that are caused by the Kelvin-Helmholtz instability. This contributes to the damping and dissipation of the transverse oscillations. Conclusions. The oscillation parameters and evolution we observed are in line with the values that are typically seen in observations of coronal loop oscillations. The dynamic evolution of the coronal loop bundle suggests that the models of monolithic and static coronal loops with constant lengths might need to be re-evaluated by relaxing the assumption of highly idealised wave guides.

Traveling kink oscillations of coronal loops launched by a solar flare

Context. Kink oscillations, which are often associated with magnetohydrodynamic waves, are usually identified as transverse displacement oscillations of loop-like structures. However, the traveling kink oscillation evolving to a standing wave has rarely been reported. Aims. We investigate the traveling kink oscillation triggered by a solar flare on 2022 September 29. The traveling kink wave is then evolved to a standing kink oscillation of the coronal loop. Methods. The observational data mainly come from the Solar Upper Transition Region Imager (SUTRI), Atmospheric Imaging Assembly (AIA), and Spectrometer/Telescope for Imaging X-rays (STIX). In order to accurately identify the diffuse coronal loops, we applied a multi-Gaussian normalization (MGN) image processing technique to the extreme ultraviolet (EUV) image sequences at SUTRI 465 Å, AIA 171 Å, and 193 Å. A sine function within the decaying term and linear trend is used to extract the oscillation periods and amplitudes. With the aid of a differential emission measure analysis, the coronal seismology is applied to diagnose key parameters of the oscillating loop. At last, the wavelet transform is used to seek for multiple harmonics of the kink wave. Results. The transverse oscillations with an apparent decay in amplitude and nearly perpendicular to the oscillating loop are observed in the passbands of SUTRI 465 Å, AIA 171 Å, and 193 Å. The decaying oscillation is launched by a solar flare erupted close to one footpoint of coronal loops and then it propagates along several loops. Next, the traveling kink wave is evolved to a standing kink oscillation. The standing kink oscillation along one coronal loop has a similar period of ∼6.3 min at multiple wavelengths, and the decaying time is estimated at ∼9.6−10.6 min. Finally, two dominant periods of 5.1 min and 2.0 min are detected in another oscillating loop, suggesting the coexistence of the fundamental and third harmonics. Conclusions. First, we report the evolution of a traveling kink pulse to a standing kink wave along coronal loops that has been induced by a solar flare. We also detected a third-harmonic kink wave in an oscillating loop.

Exact solution to the problem of slow oscillations in coronal loops and its diagnostic applications

Magnetoacoustic oscillations are nowadays routinely observed in various regions of the solar corona. This allows them to be used as means of diagnosing plasma parameters and processes occurring in it. Plasma diagnostics, in turn, requires a sufficiently reliable MHD model to describe the wave evolution. In our paper, we focus on obtaining the exact analytical solution to the problem of the linear evolution of standing slow magnetoacoustic (MA) waves in coronal loops. Our consideration of the properties of slow waves is conducted using the infinite magnetic field assumption. The main contribution to the wave dynamics in this assumption comes from such processes as thermal conduction, unspecified coronal heating, and optically thin radiation cooling. In our consideration, the wave periods are assumed to be short enough so that the thermal misbalance has a weak effect on them. Thus, the main non-adiabatic process affecting the wave dynamics remains thermal conduction. The exact solution of the evolutionary equation is obtained using the Fourier method. This means that it is possible to trace the evolution of any harmonic of the initial perturbation, regardless of whether it belongs to entropy or slow mode. We show that the fraction of energy between entropy and slow mode is defined by the thermal conduction and coronal loop parameters. It is shown for which parameters of coronal loops it is reasonable to associate the full solution with a slow wave, and when it is necessary to take into account the entropy wave. Furthermore, we obtain the relationships for the phase shifts of various plasma parameters applicable to any values of harmonic number and thermal condition coefficient. In particular, it is shown that the phase shifts between density and temperature perturbations for the second harmonic of the slow wave vary between π/2 to 0, but are larger than for the fundamental harmonic. The obtained exact analytical solution could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona.

Damping Scenarios of Kink Oscillations of Solar Coronal Loops

The transition from the large-amplitude rapidly-decaying regime of kink oscillations of plasma loops observed in the corona of the Sun to the low-amplitude decayless oscillations is modelled. In this study, the decayless regime is associated with the energy supply from coronal plasma flows, i.e., self-oscillations, or random movements of footpoints of the oscillating loop. The damping is attributed to the linear effect of resonant absorption. We demonstrate that the decay of an impulsively excited kink oscillation to the self-oscillatory stationary amplitude differs from the exponential decay. The damping time is found to depend on the oscillation amplitude to the power of a negative constant whose magnitude is less than unity. In this scenario, a better model for the damping seems to be super-exponential. In the separately considered case of the decayless oscillatory regime supported by a random driver, the oscillation amplitude experiences an exponential decay to the decayless level. Implications of this finding for magnetohydrodynamic seismology of the solar corona based on the effect of resonant absorption are discussed.

A Statistical Study of Short-period Decayless Oscillations of Coronal Loops in an Active Region

Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter, we statistically investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region (AR), i.e., NOAA AR 12965. A total of 111 coronal loops are identified in EUI 174 Å images, and they all reveal transverse oscillations without any significant decaying, regarded as decayless oscillations. Oscillatory periods are measured from ∼11 to ∼185 s, with a median period of 40 s. Thus, they are also termed short-period oscillations. The corresponding loop lengths are measured from ∼10.5 to ∼30.2 Mm, and a strong dependence of oscillatory periods on loop lengths is established, indicating that the short-period oscillations are standing kink-mode waves in nature. Based on the coronal seismology, kink speeds are measured to be ∼330–1910 km s−1, and magnetic field strengths in coronal loops are estimated to be ∼4.1–25.2 G, while the energy flux carried by decayless kink oscillations lies in the range from roughly 7 to 9220 W m−2. Our estimations suggest that the wave energy carried by short-period decayless kink oscillations cannot support the coronal heating in the AR.

Моделирование затухания нелинейных стоячих волн в высокотемпературной плазме

Longitudinal oscillations in hot post-flare coronal loops are studied in the nonlinear hydrodynamic approximation. To explain its rapid damping, the mechanism of thermal conductivity, important at high temperatures, is used. In the case of large amplitude, numerical simulations show that nonlinearity inhibits damping.