The Complex nature of magnetic element transport in the quiet sun: the Lévy-walk character

The study of the dynamic properties of small-scale magnetic fields in the solar photosphere (magnetic elements, MEs) provides a fundamental tool to investigate some still unknown aspects of turbulent convection, and gain information on the spatial and temporal scales of evolution of the magnetic field in the quiet Sun. We track the MEs in a set of magnetogram long-time series acquired by the Hinode mission, and take advantage of a method based on entropy (the diffusion entropy analysis, DEA) to detect their dynamic regime, under the assumption that MEs are passively transported by the photospheric plasma flow. DEA has been proven to perform better than other standard techniques, and for the first time it is successfully used to provide the scaling properties of the displacement of MEs in the quiet Sun. The main results of this work, which represents an extension of the analysis presented in previous literature, can be summarized as two points: (i) MEs in the quiet Sun undergo a common dynamic turbulent regime independent of the local environment; (ii) the displacement of MEs exhibits a complex transport dynamics that is consistent with a Lévy walk.