Kink Oscillations Of Coronal Loops Research Articles

Catalog of Decaying Kink Oscillations of Coronal Loops in the 24th Solar Cycle

Catalog of Decaying Kink Oscillations of Coronal Loops in the 24th Solar Cycle

Coronal Loop Seismology Using Standing Kink Oscillations With a Lookup Table

The transverse structure of coronal loops plays a key role in the physics but the small transverse scales can be difficult to observe directly. For wider loops the density profile may be estimated by forward modelling of the transverse intensity profile. The transverse density profile may also be estimated seismologically using kink oscillations in coronal loops. The strong damping of kink oscillations is attributed to resonant absorption and the damping profile contains information about the transverse structure of the loop. However, the analytical descriptions for damping by resonant absorption presently only describe the behaviour for thin inhomogeneous layers. Previous numerical studies have demonstrated that this thin boundary approximation produces poor estimates of the damping behaviour in loops with wider inhomogeneous layers. Both the seismological and forward modelling approaches suggest loops have a range of layer widths and so there is a need for a description of the damping behaviour that accurately describes such loops. We perform a parametric study of the damping of standing kink oscillations by resonant absorption for a wide range of inhomogeneous layer widths and density contrast ratios, with a focus on the values most relevant to observational cases. We describe the damping profile produced by our numerical simulations without prior assumption of its shape and compile our results into a lookup table which may be used to produce accurate seismological estimates for kink oscillation observations.

Evolution of the Transverse Density Structure of Oscillating Coronal Loops Inferred by Forward Modeling of EUV Intensity

Abstract Recent developments in the observation and modeling of kink oscillations of coronal loops have led to heightened interest over the last few years. The modification of the Transverse Density Profile (TDP) of oscillating coronal loops by nonlinear effects, particularly the Kelvin–Helmholtz Instability (KHI), is investigated. How this evolution may be detected is established, in particular, when the KHI vortices may not be observed directly. A model for the loop’s TDP is used that includes a finite inhomogeneous layer and homogeneous core, with a linear transition between them. The evolution of the loop’s transverse intensity profile from numerical simulations of kink oscillations is analyzed. Bayesian inference and forward modeling techniques are applied to infer the evolution of the TDP from the intensity profiles, in a manner that may be applied to observations. The strongest observational evidence for the development of the KHI is found to be a widening of the loop’s inhomogeneous layer, which may be inferred for sufficiently well resolved loops, i.e., >15 data points across the loop. The main signatures when observing the core of the loop (for this specific loop model) during the oscillation are a widening inhomogeneous layer, decreasing intensity, an unchanged radius, and visible fine transverse structuring when the resolution is sufficient. The appearance of these signatures are delayed for loops with wider inhomogeneous layers, and quicker for loops oscillating at higher amplitudes. These cases should also result in stronger observational signatures, with visible transverse structuring appearing for wide loops observed at the resolution of current instruments.

Spatiotemporal Analysis of Coronal Loops Using Seismology of Damped Kink Oscillations and Forward Modeling of EUV Intensity Profiles

Abstract The shape of the damping profile of kink oscillations in coronal loops has recently allowed the transverse density profile of the loop to be estimated. This requires accurate measurement of the damping profile that can distinguish the Gaussian and exponential damping regimes, otherwise there are more unknowns than observables. Forward modeling of the transverse intensity profile may also be used to estimate the width of the inhomogeneous layer of a loop, providing an independent estimate of one of these unknowns. We analyze an oscillating loop for which the seismological determination of the transverse structure is inconclusive except when supplemented by additional spatial information from the transverse intensity profile. Our temporal analysis describes the motion of a coronal loop as a kink oscillation damped by resonant absorption, and our spatial analysis is based on forward modeling the transverse EUV intensity profile of the loop under the isothermal and optically thin approximations. We use Bayesian analysis and Markov chain Monte Carlo sampling to apply our spatial and temporal models both individually and simultaneously to our data and compare the results with numerical simulations. Combining the two methods allows both the inhomogeneous layer width and density contrast to be calculated, which is not possible for the same data when each method is applied individually. We demonstrate that the assumption of an exponential damping profile leads to a significantly larger error in the inferred density contrast ratio compared with a Gaussian damping profile.

Coronal loop seismology using damping of standing kink oscillations by mode coupling

Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims. The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods. We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling. Results. Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions. This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

Motion Magnification in Coronal Seismology

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops.

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.

Dependence of kink oscillation damping on the amplitude

Context. Kink oscillations of coronal loop are one of the most ntensively studied oscillatory phenomena in the solar corona. In the large-amplitude rapidly damped regime these oscillations are observed to have a low quality-factor, with only a few cycles of oscillation detected before they are damped. The specific mechanism responsible for the rapid damping is commonly accepted to be associated with the linear coupling between collective kink oscillations and localised torsional oscillations, the phenomenon of resonant absorption of the kink mode. However, the role of finite amplitude effects is still not clear. Aims. We investigated the empirical dependence of the kink oscillation damping time and its quality factor, defined as the ratio of the damping time to the oscillation period, on the oscillation amplitude. Methods. We analysed decaying kink oscillation events detected previously with TRACE, SDO/AIA and and STEREO/EUVI in the EUV 171A band. Results. We found that the ratio of the kink oscillation damping time to the oscillation period systematically decreases with the oscillation amplitude. The quality factor dependence on the oscillation isplacement amplitude has been approximated by the powerlaw dependence with the exponent of −1/2, however we stress that this is a “by eye”estimate, and a more rigorous estimation of the scaling law requires more accurate measurements and increased statistics. We conclude that damping of kink oscillations of coronal loops depends on the oscillation amplitude, indicating the possible role of nonlinear mechanisms for damping.

Damping profile of standing kink oscillations observed by SDO/AIA

Aims: Strongly damped standing and propagating kink oscillations are observed in the solar corona. This can be understood in terms of mode coupling, which causes the wave energy to be converted from the bulk transverse oscillation to localised, unresolved azimuthal motions. The damping rate can provide information about the loop structure, and theory predicts two possible damping profiles. Methods: We used the recently compiled catalogue of decaying standing kink oscillations of coronal loops to search for examples with high spatial and temporal resolution and sufficient signal quality to allow the damping profile to be examined. The location of the loop axis was tracked, detrended, and fitted with sinusoidal oscillations with Gaussian and exponential damping profiles. Results: Using the highest quality data currently available, we find that for the majority of our cases a Gaussian profile describes the damping behaviour at least as well as an exponential profile, which is consistent with the recently developed theory for the damping profile due to mode coupling.

A statistical study of decaying kink oscillations detected using SDO/AIA

Despite intensive studies of kink oscillations of coronal loops in the last decade, a large scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO). We carry out a statistical study of kink oscillations using Extreme Ultra-Violet (EUV) imaging data from a previously compiled catalogue. We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) onboard SDO during its first four years of operation (2010-2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations. Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck =(1330+/-50) km s-1 . The main body of the data corresponds to kink speeds in the range Ck =(800-3300) km s-1. Measurements of 52 exponential damping times were made, and it was noted that at least 22 of the damping profiles may be better approximated by a combination of non-exponential and exponential profiles, rather than a purely exponential damping envelope. There are an additional 10 cases where the profile appears to be purely non-exponential, and no damping time was measured. A scaling of the exponential damping time with the period is found, following the previously established linear scaling between these two parameters.

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube.

Excitation of kink oscillations of coronal loops: statistical study

Context. Solar flares are often accompanied by kink (transverse) oscillations of coronal loops. Despite intensive study of these oscillations in recent years, the mechanisms that excite them are still not known. Aims. We aim to clarify the excitation mechanisms for these kink oscillations of coronal loops. Methods. Weanalysed 58 kink-oscillation events observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) during its first four years (2010‐2014) with the use of the JHelioviewer. Association of these oscillation events with flares, lower coronal (r 1.4R� ) eruptions and plasma ejections, coronal mass ejections (CMEs), and coronal Type-II radio bursts is studied. Results. We find that 44 of these 58 oscillation events (76%) were associated with CMEs observed in the white light emission. Moreover, 57 events (98%) were accompanied by lower coronal eruptions/ejections (LCEs) observed in the extreme-ultraviolet band in the parental active regions. In the remaining event an LCE was not clearly seen, but it was definitely associated with a CME too. The main observational finding is that the kink oscillations were excited by the deviation of loops from their equilibria by a nearby LCE in 55 events (95%). In three remaining events, it was difficult to reliably determine the cause of the oscillations because of limitations in the observational data. We also found that 53 events (91%) were associated with flares. In five remaining events, the parental active regions were behind the limb and we could not directly see flare sites. It indicates that there is a close relationship between these two kinds of solar activity. However, the estimated speeds of a hypothetical driver of kink oscillations by flares were found to be lower than 500 kms −1 in 80% of the cases. Such low speeds do not favour the association of the oscillation excitation with a shock wave, as usually assumed. That only 23 (40%) of the oscillation events were found to be associated with coronal Type-II radio bursts also goes against the shock wave mechanism for the excitation of kink oscillations. Conclusions. The statistical analysis shows that the most probable mechanism for exciting the kink oscillations of coronal loops is the deviation of loops from their equilibrium by nearby eruptions or plasma ejections rather than a blast shock wave ignited by a flare.

Non-reflective Propagation of Kink Pulses in Magnetic Waveguides in the Solar Atmosphere

We study the propagation of pulses of kink waves in magnetic-flux tubes. We use the thin-tube approximation and assume that the dependence of the phase speed on the distance along the tube is either linear or quadratic. In this case, the wave equation describing the propagation of kink waves reduces to the Klein–Gordon equation with constant coefficients. We present the general solution of the initial value–boundary value problem for this equation. Using this solution, we study the general properties of non-reflective pulse propagation. Then we apply the general results to the kink-pulse propagation in coronal magnetic loops. In particular, we suggest an alternative mechanism of small-amplitude decay-less kink oscillations in coronal loops.

Erratum to: The Effect of Loop Curvature on Coronal Loop Kink Oscillations

Erratum to: The Effect of Loop Curvature on Coronal Loop Kink Oscillations

Decay-less kink oscillations in coronal loops

Context: Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 A. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force.

Damping of coronal loop kink oscillations due to mode conversion

The damping of kink oscillations of a thin magnetic tube due to mode conversion, also called resonant absorption, is studied. The tube consists of a homogeneous core region and an inhomogeneous annulus, where the density monotonically decreases from its value in the core region to the value in the surrounding plasma. The annulus is assumed to be thin, so the study is carried out in the thin tube thin boundary approximation. The equation governing the amplitude variation of kink oscillations is derived. The initial value problem for this equation is solved to study the resonant damping. This means that, in particular, we study the transient state before the loop oscillates with the stationary or nearly stationary state. The results are compared with those of the direct numerical modelling, and the agreement is found to be fairly good. On the basis of the solution to the initial value problem for the governing equation, the damping time is calculated and compared with that given by the classical theory of resonant absorption. It is found that the classical theory underestimates the damping time, with the error increasing with the increase of the annulus thickness. However, the error is not large, so the damping time given by the classical theory of resonant absorption can be taken as a sufficiently good approximation.

BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA

The detection of multiple mode harmonic kink oscillations in coronal loops enables to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion, under each of the hypotheses. Then, the two models are compared using a Bayesian model comparison scheme to assess how plausible each one is, given our current state of knowledge.

Radiation effects on the MHD wave behavior in the solar corona

The effect of radiation losses on the dispersion and damping of magnetohydrodynamic waves in the solar corona is studied. The conditions are determined under which radiation losses are most appreciable. A damping of kink modes of coronal loops with plasma temperatures within 106–106.3 K and 106.3–107 K are compared. It is concluded that the radiation damping dominates in the temperature range 106–106.3 K, which can cause the observed fast damping of kink oscillations of coronal loops. Radiation losses should be taken into account in full magnetohydrodynamic equations with radiative transfer.

The effect of the environment on the P1/P2 period ratio for kink oscillations of coronal loops

The P1/P2 period ratio of transversal loop oscillations is currently used for the diagnostics of longitudinal structuring of coronal loops as its deviation from 2 is intrinsically connected to the density scale-height along coronal loops and/or the sub-resolution structure of the magnetic field. The same technique can be applied not only to coronal structures, but also to other oscillating magnetic structures. The oscillations in magnetic structures are described by differential equations whose coefficients depend on the longitudinal structure of the plasma. Using a variational principle written for the transversal component of the velocity vector, developed earlier by McEwan et al. (2008), we investigate how the different temperature of the environment compared to the temperature of the magnetic structure will influence the P1/P2 ratio for typical coronal and prominence conditions. The possible changes are translated into quantities that are used in the process of remote plasma diagnostics in the solar atmosphere.

Resonant damping of kink oscillations of cooling coronal magnetic loops

The simultaneous effect of amplification due to cooling and damping due to resonant absorption on the kink oscillations of coronal loops is studied. The governing equation describing the kink oscillations is derived in the thin tube thin boundary layer approximation. The cooling time is assumed to be much larger than the oscillation period, and the Wentzel-Kramers-Brillouin (WKB) method is used to obtain the equation describing the dependence of the oscillation amplitude on time. This equation is solved numerically for various values of determining parameters. In particular, the question if the amplification due to cooling can balance the resonant damping and produce undamped oscillation is addressed. The conclusion is that the amplification due to cooling is not very efficient and can balance the resonant damping only when the density contrast is not very large and the cooling is very fast with the characteristic cooling time of the order of the oscillation period.