Magnetic arcades in the solar atmosphere, or coronal loops, are common structures known to host magnetohydrodynamic (MHD) waves and oscillations. Of particular interest are the observed properties of transverse loop oscillations, such as their frequency and mode of oscillation, which have received significant attention in recent years because of their seismological capability. Previous studies have relied on standard data analysis techniques, such as a fast Fourier transform (FFT) and wavelet transform (WT), to correctly extract periodicities and identify the MHD modes. However, how these methods can lead to artefacts requires investigation. We assess whether these two common spectral analysis techniques in coronal seismology can successfully identify high-frequency waves from an oscillating coronal loop. We examine extreme ultraviolet images of a coronal loop observed by the Atmospheric Imaging Assembly in the 171 \AA waveband on board the Solar Dynamics Observatory. We perform a spectral analysis of the loop waveform and compare our observation with a basic simulation. The spectral FFT and WT power of the observed loop waveform is found to reveal a significant signal with frequency 2.67 mHz superposed onto the dominant mode of oscillation of the loop (1.33 mHz), that is, the second harmonic of the loop. The simulated data show that the second harmonic is completely artificial even though both of these methods identify this mode as a real signal. This artificial harmonic, and several higher modes, are shown to arise owing to the periodic but non-uniform brightness of the loop. We further illustrate that the reconstruction of the 2.67 mHz component in the presence of noise yields a false perception of oscillatory behaviour that does not otherwise exist. We suggest that additional techniques such as a forward model of a 3D coronal arcade are necessary to verify such high-frequency waves.

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