Quantitative Characterization of Solar Active Regions Based on Their Evolutionary Paths

We present a way of quantitatively characterizing solar active regions on the basis of their evolutionary paths. To determine characteristic properties of active regions with different sizes and configurations, we use a physics-based model to derive a relation between emerged magnetic flux and injected magnetic helicity (Flux-Helicity relation), the former of which gives scale information while the latter represents the magnetic field configuration of an active region. We demonstrate how this relation provides evolutionary paths of active regions and determines their characteristic properties, through a comparison with modeled active regions obtained from magnetohydrodynamic simulations.