Solar Flare 1/f Fluctuations from Amplitude-Modulated Five-Minute Oscillation

Abstract

We first report that the solar flare time sequence exhibits a fluctuation characterized by its power spectral density being inversely proportional to the signal frequency. This is the 1/f fluctuation, or pink noise, observed ubiquitously in nature. Using GOES16 data, we found that low-energy flares (E≤Emean) display 1/f fluctuations, whereas high-energy flares (E>Emean) show a flat spectrum. Furthermore, we found that the timing sequence of the flares reveals clearer 1/f fluctuations. These observations suggest that the solar flare 1/f fluctuations are associated with low-energy phenomena. We investigated the origin of these 1/f fluctuations based on our recent hypothesis: 1/f fluctuations arise from amplitude modulation and demodulation. We propose that this amplitude modulation is encoded by the resonance with the solar five-minute oscillation (SFO) and demodulated by magnetic reconnections. We partially demonstrate this scenario by analyzing the SFO eigenmodes resolving the frequency degeneration in the azimuthal order number m using the solar rotation and resonance. Given the robust nature of 1/f fluctuations, we speculated that the solar flare 1/f fluctuations may be inherited by the various phenomena around the Sun, such as the sunspot numbers and cosmic rays. In addition, we draw parallels between solar flares and earthquakes, both exhibiting 1/f fluctuations. Interestingly, the analysis applied to solar flares can also be adapted to earthquakes if we read the SFO as Earth’s free oscillation and magnetic reconnections as fault ruptures. Moreover, we point out the possibility that the same analysis also applies to the activity of a black hole/disk system if we read the SFO as the quasi-periodic oscillation of a black hole.

A Hybrid Model Based on CEEMDAN-GRU and Error Compensation for Predicting Sunspot Numbers

“…Thus, there is no periodicity, which is regularly manifested. (2) The relationship between datasets: Since sunspot numbers comprise a classical time series, there is an interdependence between them. (3) The delay phenomena between predictive data and original data: This problem generally exists, especially with respect to data with large fluctuations.…”

“…In the figure, we can observe that many predictive errors are very close to 0. Figure 7 shows the histogram of PE, the amount of PE with ranges at [0, 1], [1,2], [2,3], [3,4], and their counts: 320, 115, 37, 19, and 16. Therefore, this shows that most errors are clustered around 1.…”

“…Sunspots refer to the dark spots, which often appear on the sun's photosphere, and they reflect solar activity [1]. Their basic indication is the sunspot number, which is closely related to climate anomalies and the weather on earth [2,3]. When these clusters of sunspots reach their peak, they trigger solar flares and coronal mass ejections (CMEs), in which energetic particles released via solar activity flow toward the earth and interact with the earth's magnetic field, which in turn leads to geomagnetic storms.…”