Observational signatures of the third harmonic in a decaying kink oscillation of a coronal loop

Abstract

Aims. An observation of a coronal loop standing kink mode is analysed to search for higher harmonics, aiming to reveal the relation between different harmonics’ quality factors. Methods. Observations of a coronal loop were taken by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The loop’s axis was tracked at many spatial positions along the loop to generate time series data. Results. The distribution of spectral power of the oscillatory transverse displacements throughout the loop reveals the presence of two harmonics, a fundamental at a period of ∼8 min and its third harmonic at ∼2.6 min. The node of the third harmonic is seen at approximately a third of the way along the length of the loop, and cross correlations between the oscillatory motion on opposing sides of the node show a change in phase behaviour. The ratio of periods P1/3P3 was found to be ∼0.87, indicating a non-uniform distribution of kink speed through the loop. The quality factor for the fundamental mode of oscillation was measured to be ∼3.4. The quality factor of the third harmonic was measured for each spatial location and, where data was reliable, yielded a value of ∼3.6. For all locations, the quality factors for the two harmonics were found to agree within error as expected from 1d resonant absorption theory. This is the first time a measurement of the signal quality for a higher harmonic of a kink oscillation has been reported with spatially resolved data.

Tracking and Seismological Analysis of Multiple Coronal Loops in an Active Region

“…Several studies have revealed the presence of additional higher longitudinal harmonics (e.g. Van Doorsselaere et al 2007;Pascoe et al 2016a;Duckenfield et al 2018Duckenfield et al , 2019. Since our slit is located at the loop apex, we might also expect to observe the third harmonic, assuming the main oscillation is the fundamental, but we found no evidence of a higher frequency component in our tests.…”

Oscillation and Evolution of Coronal Loops in a Dynamical Solar Corona

“…The presence of longitudinal stratification due to gravity, expansion, or curvature leads to coupling of longitudinal harmonics (e.g., Pascoe et al, 2009;Pascoe and Nakariakov, 2016) and changes to the ratio of their periods (e.g., Andries et al, 2005;McEwan et al, 2006;Safari et al, 2007;Verth and Erdélyi, 2008;Arregui et al, 2013) but does not significantly affect the damping rate due to resonant absorption (Arregui et al, 2005;Dymova and Ruderman, 2006). The period ratio for harmonics has been observed in many studies of large-amplitude oscillations (e.g., Verwichte et al, 2004;De Moortel and Brady, 2007;Van Doorsselaere et al, 2007;Pascoe et al, 2016aPascoe et al, , 2017aDuckenfield et al, 2019) and recently in decayless oscillations (Duckenfield et al, 2018). Figure 1 shows the evolution of the transverse loop density profile at the middle of the coronal loop, i.e., the antinode for the fundamental standing kink mode.…”

The need for new techniques to identify the high-frequency MHD waves of an oscillating coronal loop

“…Furthermore, we validate our initial FFT analysis and account for any non-stationary signals that may be present within the data by performing a wavelet analysis (Torrence & Compo 1998). This technique is often preferred over a traditional FFT analysis in coronal seismic studies owing to its ability to distinguish both the frequency and temporal content of a given signal (e.g., Duckenfield et al 2019;Pascoe et al 2020). We also relax the assumption of a white noise background in our wavelet analysis to account for any frequency dependence from the data and estimate the corresponding 95% confidence levels of the wavelet power.…”

“…A significant improvement in the spatial and temporal resolutions of the detector may also be necessary to convincingly identify high-frequency modes from observations. Finally, we comment on the validity of searching for loop overtones from observations (e.g., Pascoe et al 2016;Duckenfield et al 2019). Such studies extract the dominant (foreground) signal before conducting a spectral analysis using either FFT or WTs by estimating the position of peak brightness as a function of time where the projected loop exhibits a clear phase difference (also see Verwichte et al 2009).…”

“…The primary interest in understanding the mode of oscillation of a loop lies in its seismological capability when used in tandem with 1D models (Andries et al 2005). Often, the approach is to compute the ratio of a loop's observed fundamental period P 1 to its nth overtone, that is P 1 /nP n (Duckenfield et al 2018(Duckenfield et al , 2019. For a dispersion-less oscillation, it is believed that any deviation of this period ratio from unity may suggest a plasma density stratification within the loop (Andries et al 2009).…”