Magnetic Helicity and Free Magnetic Energy of two Differently Evolving Solar Active Regions

Free magnetic energy (that is relating to the electric current density) and relative magnetic helicity are key parameters that characterize the magnetic field in the solar atmosphere. The former is released in the course of flares, coronal mass ejections (CMEs), and smaller-scale dissipative events while the latter can either be removed from active regions in the form of CMEs or is transferred during reconnection events to larger-scales via existing magnetic connections. Using vector magnetograms obtained by the Helioseismic and Magnetic Imager (HMI) on board Solar Dynamics Observatory (SDO), and a connectivity-based method, we calculate the instantaneous relative magnetic helicity and free magnetic energy budgets for several days in two active regions with significantly different magnetic flux evolution. Both active regions produced several major flares associated with -CMEs during their disk passage, but this activity resulted from very different magnetic evolution: primarily magnetic flux cancellation in the first active region and primarily magnetic flux emergence in the second one. We will present the results of these calculations which show: (1) the existence of reversals in the sign of helicity before or/and after several CMEs. (2) CMEs occurring while the net active region helicities are below previously established thresholds (~2×10⁴² Mx²) but both their positive and (absolute) negative components are significant. (3) The free magnetic energy exhibits substantial budgets whose long-term evolution is similar to the long-term evolution of the active region's magnetic flux, although this is not always the case around large eruptive events. Our study indicates that although the two active regions evolve differently, their magnetic helicity and free magnetic energy play important roles in the initiation of their eruptive events.