Generalized Laplacian for magnetograms of solar active region as possible predictor of strong flare.

International Conference on Particle Physics and Astrophysics

Volobuev, D.M.^1 ; Makarenko, N.G.^1 ; Knyazeva, I.S.^1

Pulkovo Observatory, Pulkovskoye shosse 65, Saint-Petersburg, Russia^1

关键词: Betti numbers;    Low probability;    Polarity inversion lines;    Ricci curvature;    Solar active regions;    Solar physics;    Spatial variations;    Topological invariants;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/675/3/032027/pdf
DOI  :  10.1088/1742-6596/675/3/032027

来源: IOP

【 摘 要 】

Search for predictors of strong flare produced in solar active region (AR) is important application of solar physics. Here we consider the sequence of magnetogram (LOS SDO/HMI instrument) for AR 2034, 2035 and 2036 (April 2014). All three AR were observed on the Sun at about the same time, characterized by low probability of flare events according to official forecasts of NOAA, but 2036 still produced X1-flare near the center of solar disc (April 18). We propose that Generalized Laplacian is a descriptor which could help predict this and similar events. The Laplacian is associated with the flow of Ricci curvature and with topological invariants of the observed field - Betti numbers for compact manifolds. Using discrete version of Morse theory, we consider each pixel of energy flux (B2) image as a simplex and calculate its combinatorial Bochner Laplacian. It was found that maximum of Laplacian is located near AR polarity inversion line. Evolution of total spatial variation of the Laplacian has a number of maxima in time for each of examined AR. However, the maxima in AR 2035 and AR 2034 have relatively low amplitude, while the highest maximum prefaced X1 flare in AR 2036 by about 29 hours.