Magnetic energy balance in the quiet sun on supergranular spatial and temporal scales

Small-scale magnetic fields are ubiquitous in the quiet solar photosphere and may store and transfer huge amounts of energy to the upper atmospheric layers. For this reason, it is fundamental to constrain the energetics of the quiet Sun. By taking advantage of a 24 hr long magnetogram time series acquired by the Hinode mission without interruption, we computed, for the first time, the average rate of change of magnetic energy density on supergranular spatial and temporal scales. We found that the regions where this quantity is positive correspond with the longest magnetic field decorrelation times, with the latter being consistent with the timescales of magnetic energy density variation. This suggests that, on average, the energy provided by photospheric electric and magnetic fields and current density is effective in sustaining the magnetic fields in the network.