The Complex Nature of Magnetic Element Transport in the Quiet Sun: The Multiscaling Character

In recent studies the dynamic properties of small-scale magnetic fields (magnetic elements [MEs]) in the quiet Sun were used to investigate peculiar features of turbulent convection and get insights on the characteristic spatial and temporal scales of evolution of magnetic fields, from granular to supergranular. The aim of this work is to extend previous studies and show that the displacement of MEs is compatible with a multiscaling behavior consistent with a Lévy motion. We tracked over 120,000 MEs in an unprecedented and uninterrupted set of high-resolution magnetograms acquired by the Hinode mission and targeted at quiet-Sun regions in the disk center, and we applied the multifractal diffusion entropy analysis to investigate the multiscaling character of ME transport in the quiet Sun. We found that the displacement of MEs in the quiet Sun exhibits a complex multiscaling behavior that cannot be described by a unique scaling law, as scaling exponents change with the scale considered. This result adds important physical constraints on turbulent convection and diffusion of MEs in the quiet Sun that future models need to account for.