Transverse Coronal Loop Oscillations Research Articles

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.

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.

The probable excitation mechanism of kink oscillations of coronal loops

Oscillations in various structures of the solar atmosphere, such as transverse (kink) oscillations of coronal loops, can be used in seismology. Transvers kink oscillations of coronal loops are often accompanied by solar flares. Despite the intensive study of kink oscillations of coronal loops in recent years, the excitation mechanism of these oscillations are still not known. In this paper, we aim to clarify the excitation mechanisms of transverse oscillations of coronal loops. For this purpose, first 458 oscillation events were identified by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) during its first ten years (2010–2019) with the use of the Helioviewer, JHelioviewer and Heliophysics Events Knowledgebase (HEK). Then, the association of these oscillation events with probable mechanism for exciting the kink oscillations such as flares, lower coronal eruptions and plasma ejections, and coronal mass ejections bursts were listed. Finally, about 138 suitable kink oscillations out of 485 oscillations with high-amplitude, long oscillation period and visible through the naked eye that were accompanied with other probable excitation mechanism of kink oscillations, were selected. This statistical analysis of the transverse oscillation coronal loops showed that that 102 of these 138 oscillation events (74 %) were associated with lower coronal eruptions or plasma ejections. About 38 oscillations out of 138 transverse oscillations (27.5%) were associated with coronal mass ejections/eruption. Also, 65 events (47 %) were associated with flares. The required speed of hypothetical drivers of transverse oscillations were calculated. The magnitude values of calculated speeds for shock wave of flares were found to be lower than 500±100 km/s in 87% of the cases. Also, the magnitude values of speeds for lower coronal mass eruption/ejection were obtained to be lower than 500±125 km/s in 94% of the cases. The magnitude values of these speeds are acceptable for lower coronal mass eruption/ejection. But, such low speeds do not favor the association of the oscillation excitation with a shock wave of flares, as usually assumed. Also, statistical analysis of start time and time difference of hypothetical drivers of transverse oscillations showed that there is no clear correlation between them. The results of this study indicated that shock wave of flares cannot be the main cause of transverse oscillations of coronal loops. So, this analysis shows that the most probable excitation mechanism of the kink oscillations of coronal loops are eruptions or plasma ejections rather than the blast shock waves ignited by flares. ‎

Exploring the Ideal MHD Quasi-Modes of a Plasma Interface with a Thick Nonuniform Transition

Nonuniform plasma across an imposed magnetic field, such as those present in the solar atmosphere, can support collective Alfvénic oscillations with a characteristic damping time. The damped transverse oscillations of coronal loops are an example of this process. In ideal magnetohydrodynamics (MHD), these transient collective motions are associated with quasi-modes resonant in the Alfvén continuum. Quasi-modes live in a non-principal Riemann sheet of the dispersion relation, and so they are not true ideal MHD eigenmodes. The present study considers the illustrative case of incompressible surface MHD waves propagating on a nonuniform interface between two uniform plasmas with a straight magnetic field parallel to the interface. It is explored how the ideal quasi-modes of this configuration change when the width of the nonuniform transition increases. It is found that interfaces with wide enough transitions are not able to support truly collective oscillations. A quasi-mode that can be related with a resonantly damped surface MHD wave can only be found in interfaces with sufficiently thin transitions.

Study of Transverse Oscillations in Coronal Loops Excited by Flares and Eruptions

We present measurements of periodicity for transverse loop oscillations during the periods of activity of two remote and separated (both temporally and spatially) flares. The oscillations are observed in the same location more than 100 Mm away from the visible footpoints of the loops. Evidence for several possible excitation sources is presented. After close examination, we find that the eruptions during the flaring activities play an important role in triggering the oscillations. We investigate periodicities using time–distance, fast Fourier transform, and wavelet techniques. Despite different excitation sources in the vicinity of the loops and the changing nature of amplitudes, the periodicity of multiple oscillations is found to be 4–6 min.

Forward Modeling of Simulated Transverse Oscillations in Coronal Loops and the Influence of Background Emission

Abstract 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.

Transverse Loop Oscillations via Vortex Shedding: A Self-oscillating Process

Abstract Identifying the underlying mechanisms behind the excitation of transverse oscillations in coronal loops is essential for their role as diagnostic tools in coronal seismology and their potential use as wave heating mechanisms of the solar corona. In this paper, we explore the concept of these transverse oscillations being excited through a self-sustaining process, caused by Alfvénic vortex shedding from strong background flows interacting with coronal loops. We show for the first time in 3D simulations that vortex shedding can generate transverse oscillations in coronal loops, in the direction perpendicular to the flow due to periodic “pushing” by the vortices. By plotting the power spectral density we identify the excited frequencies of these oscillations. We see that these frequencies are dependent both on the speed of the flow, as well as the characteristics of the oscillating loop. This, in addition to the fact that the background flow is constant and not periodic, makes us treat this as a self-oscillating process. Finally, the amplitudes of the excited oscillations are near constant in amplitude, and are comparable with the observations of decay-less oscillations. This makes the mechanism under consideration a possible interpretation of these undamped waves in coronal loops.

Simultaneous transverse oscillations of a coronal loop and a filament excited by a circular-ribbon flare

Aims. The aim of this study is to investigate the excitation of kink oscillations in coronal loops and filaments, by analyzing a C3.4 circular-ribbon flare associated with a blowout jet in active region 12434 on 2015 October 16. Methods. The flare was observed in ultraviolet and extreme-ultraviolet wavelengths by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO) spacecraft. The line-of-sight (LOS) magnetograms of the photosphere were observed by the Helioseismic and Magnetic Imager on board SDO. Soft X-ray fluxes of the flares in 0.5−4 and 1−8 Å were recorded by the GOES spacecraft. Results. The flare excited small-amplitude kink oscillation of a remote coronal loop. The oscillation lasted for ≥4 cycles without significant damping. The amplitude and period are 0.3 ± 0.1 Mm and 207 ± 12 s. Interestingly, the flare also excited transverse oscillation of a remote filament. The oscillation lasted for ∼3.5 cycles with decaying amplitudes. The initial amplitude is 1.7−2.2 Mm. The period and damping time are 437−475 s and 1142−1600 s. The starting times of simultaneous oscillations of coronal loop and filament were concurrent with the hard X-ray peak time. Though small in size and short in lifetime, the flare set off a chain reaction. It generated a bright secondary flare ribbon (SFR) in the chromosphere, remote brightening (RB) that was cospatial with the filament, and intermittent, jet-like flow propagating in the northeast direction. Conclusions. The loop oscillation is most probably excited by the flare-induced blast wave at a speed of ≥1300 km s−1. The excitation of the filament oscillation is more complicated. The blast wave triggers secondary magnetic reconnection far from the main flare, which not only heats the local plasma to higher temperatures (SFR and RB), but produces jet-like flow (i.e., reconnection outflow) as well. The filament is disturbed by the secondary magnetic reconnection and experiences transverse oscillation. These findings provide new insight into the excitation of transverse oscillations of coronal loops and filaments.

Generating Transverse Loop Oscillations through a Steady-flow Driver

Abstract In recent years, the decay-less regime of standing transverse oscillations in coronal loops has been the topic of many observational and numerical studies, focusing on their physical characteristics, as well as their importance for coronal seismology and wave heating. However, no definitive answer has yet been given on the driving mechanism behind these oscillations, with most studies focusing on the use of periodic footpoint drivers as a means to excite them. In this paper, our goal is to explore the concept of these standing waves being self-sustained oscillations, driven by a constant background flow. To that end, we use the PLUTO code, to perform 3D magnetohydrodynamic simulations of a gravitationally stratified straight flux tube in a coronal environment, in the presence of a weak flow around the loop, perpendicular to its axis. Once this flow is firmly set up, a transverse oscillation is initiated, dominated by the fundamental kink mode of a standing wave, while the existence of a second harmonic is revealed, with a frequency ratio to the fundamental mode near the observed ones in decay-less oscillations. The presence of vortex shedding is also established in our simulations, which is connected to the “slippery” interaction between the oscillator and its surrounding plasma. We thus present a proof-of-concept of a self-oscillation in a coronal loop, and we propose it as a mechanism that could interpret the observed decay-less transverse oscillations of coronal loops.

Transverse coronal loop oscillations excited by homologous circular-ribbon flares

Aims. We report our multiwavelength observations of two homologous circular-ribbon flares in active region 11991 on 2014 March 5, focusing on the transverse oscillations of an extreme-ultraviolet (EUV) loop excited by the flares. Methods. The flares were observed in ultraviolet and EUV wavelengths by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory spacecraft. These flares were also observed in Hα line center by the 1 m New Vacuum Solar Telescope. Soft X-ray fluxes of the flares in 0.5–4 and 1–8 Å were recorded by the GOES spacecraft. Results. The transverse oscillations are of fast standing kink mode. The first-stage oscillation triggered by the C2.8 flare is decayless with lower amplitudes (310–510 km). The periods (115–118 s) in different wavelengths are nearly the same, indicating coherent oscillations. The magnetic field of the loop is estimated to be 65–78 G. The second-stage oscillation triggered by the M1.0 flare is decaying with larger amplitudes (1250–1280 km). The periods decrease from 117 s in 211 Å to 70 s in 171 Å, implying a decrease of loop length or an implosion after a gradual expansion. The damping time, which is 147–315 s, increases with the period, so that the values of τ/P are close to each other in different wavelengths. The thickness of the inhomogeneous layer is estimated to be ∼0″​​​.45 under the assumption of resonant absorption. Conclusions. This is the first observation of the excitation of two kink-mode loop oscillations by two sympathetic flares. The results are important to understand the excitation of kink oscillations of coronal loops and hence the energy balance in the solar corona. Our findings also validate the prevalence of significantly amplified amplitudes of oscillations by successive drivers.

Excitation of decay-less transverse oscillations of coronal loops by random motions

Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic 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. Aims. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. Methods. 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 considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise. Results. We 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 the generation of multiple harmonics detected recently. Conclusions. We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.

Wave Heating in Simulated Multistranded Coronal Loops

Abstract It has been found that the Kelvin–Helmholtz instability (KHI) induced by both transverse and torsional oscillations in coronal loops can reinforce the effects of wave heating. In this study, we model a coronal loop as a system of individual strands, and we study wave heating effects by considering a combined transverse and torsional driver at the loop footpoint. We deposit the same energy into the multistranded loop and an equivalent monolithic loop, and then observe a faster increase in the internal energy and temperature in the multistranded model. Therefore, the multistranded model is more efficient in starting the heating process. Moreover, higher temperature is observed near the footpoint in the multistranded loop and near the apex in the monolithic loop. The apparent heating location in the multistranded loop agrees with the previous predictions and observations. Given the differences in the results from our multistranded loop and monolithic loop simulations, and given that coronal loops are suggested to be multistranded on both theoretical and observational grounds, our results suggest that the multistrandedness of coronal loops needs to be incorporated in future wave-based heating mechanisms.

Normal Modes of Transverse Coronal Loop Oscillations from Numerical Simulations. I. Method and Test Case

Abstract The purpose of this work is to develop a procedure to obtain the normal modes of a coronal loop from time-dependent numerical simulations with the aim of better understanding observed transverse loop oscillations. To achieve this goal, in this paper we present a new method and test its performance with a problem for which the normal modes can be computed analytically. In a follow-up paper, the application to the simulations of Rial et al. is tackled. The method proceeds iteratively and at each step consists of (i) a time-dependent numerical simulation followed by (ii) the Complex Empirical Orthogonal Function (CEOF) analysis of the simulation results. The CEOF analysis provides an approximation to the normal mode eigenfunctions that can be used to set up the initial conditions for the numerical simulation of the following iteration, in which an improved normal mode approximation is obtained. The iterative process is stopped once the global difference between successive approximate eigenfunctions is below a prescribed threshold. The equilibrium used in this paper contains material discontinuities that result in one eigenfunction with a jump across these discontinuities and two eigenfunctions whose normal derivatives are discontinuous there. After six iterations, the approximations to the frequency and eigenfunctions are accurate to ≲0.7% except for the eigenfunction with discontinuities, which displays a much larger error at these positions.

Contribution of observed multi frequency spectrum of Alfvén waves to coronal heating

Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. Aims. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. Methods. We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum. Results. We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin–Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. Conclusions. This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.

An Analytical Model of the Kelvin–Helmholtz Instability of Transverse Coronal Loop Oscillations

Abstract Recent numerical simulations have demonstrated that transverse coronal loop oscillations are susceptible to the Kelvin–Helmholtz (KH) instability due to the counterstreaming motions at the loop boundary. We present the first analytical model of this phenomenon. The region at the loop boundary where the shearing motions are greatest is treated as a straight interface separating time-periodic counterstreaming flows. In order to consider a twisted tube, the magnetic field at one side of the interface is inclined. We show that the evolution of the displacement at the interface is governed by Mathieu’s equation, and we use this equation to study the stability of the interface. We prove that the interface is always unstable and that, under certain conditions, the magnetic shear may reduce the instability growth rate. The result, that the magnetic shear cannot stabilize the interface, explains the numerically found fact that the magnetic twist does not prevent the onset of the KH instability at the boundary of an oscillating magnetic tube. We also introduce the notion of the loop σ-stability. We say that a transversally oscillating loop is σ-stable if the KH instability growth time is larger than the damping time of the kink oscillation. We show that even relatively weakly twisted loops are σ-stable.

Observations of Excitation and Damping of Transversal Oscillations in Coronal Loops by AIA/SDO

The excitation and damping of transversal coronal loop oscillations and quantitative relation between damping time, damping quality (damping time per period), oscillation amplitude, dissipation mechanism and the wake phenomena are investigated. The observed time series data with the \textit{Atmospheric Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory} (SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12 seconds cadence in the 171 $ \rm{{\AA}}$ pass band is analyzed for evidence of transversal oscillations along the coronal loops by Lomb-Scargle periodgram. In this analysis signatures of transversal coronal loop oscillations that are damped rapidly were found with dominant oscillation periods in the range of $\rm{P=12.25-15.80}$ minutes. Also, damping times and damping qualities of transversal coronal loop oscillations at dominant oscillation periods are estimated in the range of $ \rm{\tau_d=11.76-21.46}$ minutes and $ \rm{\tau_d/P=0.86-1.49}$, respectively. The observational results of this analysis show that damping qualities decrease slowly with increasing the amplitude of oscillation, but periods of oscillations are not sensitive function of amplitude of oscillations. The order of magnitude of the damping qualities and damping times are in good agreement with previous findings and the theoretical prediction for damping of kink mode oscillations by dissipation mechanism. Furthermore, oscillation of loop segments attenuate with time roughly as $t^{-\alpha}$ that magnitude values of $\alpha$ for 30 different segments change from 0.51 to 0.75.

Heating by transverse waves in simulated coronal loops

Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The nonlinear nature of the mechanism has been examined alongside the Kelvin-Helmholtz instability, which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Using the MPI-AMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. We have observed the development of Kelvin-Helmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.

Undamped transverse oscillations of coronal loops as a self-oscillatory process

Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes, the rapidly decaying large amplitude oscillations, and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude. Different loops oscillate with different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period. Aims. We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, e.g. supergranulation motions near the loop footpoints or external flows in the corona. Methods. We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a nonlinear ordinary differential equation, with the damping and resonant terms determined empirically. Results. Low-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition at the frequency of the natural oscillation. Conclusions. We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, in analogy with producing a tune by a stick moving across a violin string.