Diffusion of magnetic elements in a supergranular cell

Small scale magnetic fields (magnetic elements) are ubiquitous in the solar photosphere. Their interaction can provide energy to the upper atmospheric layers, and contribute to heat the solar corona. In this work, the dynamic properties of magnetic elements in the quiet Sun are investigated. The high number of magnetic elements detected in a supegranular cell allowed us to compute their displacement spectrum $\langle(\Delta r)^2\rangle\propto\tau^\gamma$ (being $\gamma>0$, and $\tau$ the time since the first detection), separating the contribution of the network (NW) and the internetwork (IN) regions. In particular, we found $\gamma=1.27\pm0.05$ and $\gamma=1.08\pm0.11$ in NW (at smaller and larger scales, respectively), and $\gamma=1.44\pm0.08$ in IN. These results are discussed in light of the literature on the topic, as well as the implications for the build up of the magnetic network.