C. R. Goddard

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

Context. 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). Aims. We carry out a statistical study of kink oscillations using extreme ultraviolet imaging data from a previously compiled catalogue. Methods. We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) on board 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. Results. 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 21 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 nine additional 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.

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.

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

Context. Kink oscillations of solar coronal loops are frequently observed to be strongly damped. The damping can be explained by mode coupling on the condition that loops have a finite inhomogeneous layer between the higher density core and lower density background. The damping rate depends on the loop density contrast ratio and inhomogeneous layer width. Aims. The theoretical description for mode coupling of kink waves has been extended to include the initial Gaussian damping regime in addition to the exponential asymptotic state. Observation of these damping regimes would provide information about the structuring of the coronal loop and so provide a seismological tool. Methods. We consider three examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) for which the general damping profile (Gaussian and exponential regimes) can be fitted. Determining the Gaussian and exponential damping times allows us to perform seismological inversions for the loop density contrast ratio and the inhomogeneous layer width normalised to the loop radius. The layer width and loop minor radius are found separately by comparing the observed loop intensity profile with forward modelling based on our seismological results. Results. The seismological method which allows the density contrast ratio and inhomogeneous layer width to be simultaneously determined from the kink mode damping profile has been applied to observational data for the first time. This allows the internal and external Alfven speeds to be calculated, and estimates for the magnetic field strength can be dramatically improved using the given plasma density. Conclusions. The kink mode damping rate can be used as a powerful diagnostic tool to determine the coronal loop density profile. This information can be used for further calculations such as the magnetic field strength or phase mixing rate.

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.

Coronal loop seismology using damping of standing kink oscillations by mode coupling II. additional physical effects and Bayesian analysis

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.

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

We consider a coronal loop kink oscillation observed by the atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics. Methods. We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the detrended displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs. Results. We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 “ 5.00 ˘ 0.62 minutes, P2 “ 2.20 ˘ 0.23 minutes, P1{2P2 “ 1.15 ˘ 0.22, and τ{P “ 3.35 ˘ 1.45.

Observation of quasi-periodic solar radio bursts associated with propagating fast-mode waves

Radio emission observations from the Learmonth and Bruny Island radio spectrographs are analysed to determine the nature of a train of discrete, periodic radio \lq sparks\rq (finite-bandwidth, short-duration isolated radio features) which precede a type II burst. We analyse extreme ultraviolet (EUV) imaging from SDO/AIA at multiple wavelengths and identify a series of quasi-periodic rapidly-propagating enhancements, which we interpret as a fast wave train, and link these to the detected radio features. The speeds and positions of the periodic rapidly propagating fast waves and the coronal mass ejection (CME) were recorded using running-difference images and time-distance analysis. From the frequency of the radio sparks the local electron density at the emission location was estimated for each. Using an empirical model for the scaling of density in the corona, the calculated electron density was used to obtain the height above the surface at which the emission occurs, and the propagation velocity of the emission location. The period of the radio sparks,

Coronal loop density profile estimated by forward modelling of EUV intensity

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A statistical study of the inferred transverse density profile of coronal loop threads observed with SDO/AIA

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Seismology of contracting and expanding coronal loops using damping of kink oscillations by mode coupling

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