| Auteur(s) supplémentaire(s) | Froment, C. Bocchialini, K., Solomon, J., Buchlin, E. |
Abstract | We present a detailed analysis of the properties of the Fourier and wavelet power spectra of slow periodic pulsations observed in solar coronal loops and described by Froment et al. Our primary aim was to re-assess critically the significance of the detections. This requires proper estimation of the frequency dependence and statistical properties of the several components constituting the power spectra. This includes recognition of the possible modification of the spectral shape by pre-processing of the data. We demonstrate that de-trending tends to produce false detections around the frequency cut-off of the applied filter. In addition, we show that the models of white and red noise built in the widely used wavelet code of Torrence & Compo in most cases cannot adequately represent the power spectrum of coronal time series, thus also possibly leading to false positives. Both effects suggest that several reports of periodic phenomena in the corona should be re-examined.
However, the Torrence & Compo code effectively computes rigorous confidence levels if it is fed with pertinent models of mean power spectra, and we give practical information on the corresponding manner to call the core routines. We remind the meaning of the default confidence levels output by the code and we propose new Monte Carlo-derived confidence levels that take into account the total number of degrees of freedom in the wavelet spectra. In this way, we confirm that the peaks of power detected by Froment et al. in extreme-ultraviolet light curves from the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) telescope have less than 0.1% chance of being caused by stochastic processes. We further show that, in addition to the power law expected from a background stochastic process, the power spectra exhibit the discrete harmonics and continuous component characteristic of signals formed by periodic pulses of random amplitudes.
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