Modelling graph dynamics of flaring active regions using SDO/HMI data

Abstract

Large solar flares define parameters of space weather near the Earth and normal operation of spacecrafts substantially depends on the cosmic particles flux of solar wind. Therefore, search for large flares predictors is an important problem. We propose to approximate topology of the magnetic field of active region by graph, whose vertices are minima and maxima of a scalar field and edges form a so-called critical net. Localization and number of critical points change during the process of evolution and, therefore, it is possible to track dynamic regimes of active region by considering dynamics of graphs. Numerical characteristic of the critical net is a spectrum of eigenvalues of its discrete Laplacian. We present examples which show that, apparently, Laplacian spectrum is closely related to flaring activity. It will allow us to use critical net in prognostic systems for prediction of large solar flares.