We study the effect of newly emerged solar active regions (ARs) on the large-scale magnetic environment of pre-existing ARs (PEARs). We first present a theoretical approach to quantify the interaction energy between new ARs and PEARs as the difference between (i) the summed magnetic energies of their individual potential fields and (ii) the energy of their superposed potential fields. We expect that this interaction energy can, depending upon the relative arrangements of newly emerged and PEAR magnetic flux, indicate the existence of topological free magnetic energy in the global coronal field that is independent of any internal free magnetic energy due to coronal electric currents flowing within the newly emerged and PEAR flux systems. We then examine the interaction energy in two well-studied cases of flux emergence, but find that the predicted energetic perturbation is relatively small compared to energies released in large solar flares. Next, we present an observational study on the influence of the emergence of new ARs on flare statistics in PEARs, using NOAAs Solar Region Summary and GOES flare databases. As part of an effort to precisely determine the emergence time of ARs in a large event sample, we find that emergence in about half of these regions exhibits a two-stage behavior, with an initial gradual phase followed by a more rapid phase. Regarding flaring, we find that the emergence of new ARs is associated with a significant increase in the occurrence rate of X- and M-class flares in PEARs. This effect tends to be more significant when PEARs and new emerging ARs are closer. Given the relative weakness of the interaction energy, this effect suggests that perturbations in the large-scale magnetic field, such as topology changes invoked in the breakout model of coronal mass ejections, might play a significant role in the occurrence of some flares.
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