Evolution of the Bochner Laplacian for magnetograms of solar active regions

A search for powerful flare predictors remains a problem of current interest in solar—terrestrial physics. The magnetograms (LOS SDO/HMI instrument) for active regions (ARs) 1158, 1166, 1283, and 1520, which produced an X-ray flare located near the central meridian, are analyzed. AR 1654, which was rather complex but generated only M flares near western limb, remaining quiet during the passage over the disk, has been analyzed in a similar manner for comparison. The combinatorial Bochner Laplacian was used as a complexity descriptor. We calculate it for each magnetogram, which was converted into the magnetic energy density of the longitudinal field component, and analyze its maximal spatial variation. It has been shown that the maximal spatial Laplacian values trace the neutral line during AR evolution, demonstrating sharp peaks before and after the flare in this case. Although this signature has no established statistical reliability, it can be interesting as an effective parameter when flares are predicted.