Energy and helicity budgets of solar quiet regions

Aims. We investigate the free magnetic energy and relative magnetic helicity budgets of solar quiet regions. Methods. Using a novel nonlinear force-free method that requires single solar vector magnetograms we calculated the instantaneous free magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector magnetograms. Results. As in a previous work on active regions, we constructed here for the first time the (free) energy-(relative) helicity diagram of quiet-Sun regions. We find that quiet-Sun regions have no dominant sense of helicity and show monotonic correlations a) between free magnetic energy/relative helicity and magnetic network area and, consequently, b) between free magnetic energy and helicity. Free magnetic energy budgets of quiet-Sun regions represent a rather continuous extension of respective active-region budgets towards lower values, but the corresponding helicity transition is discontinuous because of the incoherence of the helicity sense in contrast to active regions. We furthermore estimated the instantaneous free magnetic-energy and relative magnetic-helicity budgets of the entire quiet Sun, as well as the respective budgets over an entire solar cycle. Conclusions. Derived instantaneous free magnetic energy budgets and, to a lesser extent, relative magnetic helicity budgets over the entire quiet Sun are similar to the respective budgets of a sizeable active region, while total budgets within a solar cycle are found to be higher than previously reported. Free-energy budgets are similar to the energy needed to power fine-scale structures residing at the network, such as mottles and spicules.