Exploring the Transition to a Critical State in Active Regions via Natural Time Analysis

Abstract Solar flares are driven by the sudden release of magnetic energy when an active region (AR) reaches a topologically unstable, critical state. Identifying this exact transition is fundamentally challenging, as quantitative predictive models relying on extensive magnetic parameters inherently scale with the AR’s macroscopic size and total energy reservoir. To decouple the dynamical organization of the magnetic field from its mere total magnitude, natural time analysis (NTA) is applied for the first time to photospheric magnetic indices. High-cadence time series of Space-weather Helioseismic and Magnetic Imager Active Region Patch features for a statistical sample of 20 ARs (10 highly flare-productive and 10 flare-quiet regions) are remapped into the natural time domain. To explicitly demonstrate that NTA is independent of the AR’s absolute macroscopic scale, the sample includes statistical anomalies, such as a relatively small, simple β region that produced strong M-class flares and a large, complex region that remained quiet. The analysis reveals that extensive parameters tracking the accumulation of organized currents, magnetic helicity, and free energy exhibit distinctive behaviors in the NTA order parameter ( κ 1 ) and dynamic entropy ( S ) into critical regimes, showing an intrinsic temporal difference relative to the onset of major M- and X-class eruptions. Conversely, intensive mean-field descriptors remain comparatively insensitive, and the nonflaring control region shows no critical signatures. These findings support a physical scenario in which the continuous emergence of dynamo-generated twisted flux and polarity inversion line-aligned shearing progressively inject current-carrying structures into the atmosphere. NTA effectively captures the epoch when this accumulated stress reorganizes into a critically correlated configuration susceptible to macroscopic magnetohydrodynamic instabilities, providing a rigorous, size-independent diagnostic for understanding flare initiation.