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

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 simple model for pink noise from amplitude modulations.

We propose a simple model for the origin of pink noise (or 1/f fluctuation) based on the waves with accumulating frequencies. These waves arise spontaneously in a system with synchronization, resonance, and infrared divergence. Many waves with accumulating frequencies can produce signals of arbitrary small frequencies from a system of small size. This beat mechanism can be understood as amplitude modulation. The pink noise can appear after the demodulation process, which produces a variety of pink noise in many fields. The pink noise thus formed from the beat has nothing to do with dissipation or long-time memory. We also suggest new ways of looking at pink noise in earthquakes, solar flares, and stellar activities.

Local virial relation for self-gravitating system.

We demonstrate that the quasi-equilibrium state in a self-gravitating N-body system after cold collapse is uniquely characterized by the local virial relation using numerical simulations. Conversely, assuming the constant local virial ratio and Jeans equation for a spherically steady-state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Specifically, the local virial relation always provides a solution which has a power-law density profile in both the asymptotic regions r --> 0 and infinity. This type of solution is commonly observed in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.

Universal non-Gaussian velocity distribution in violent gravitational processes.

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.