Scaling properties of magnetic field fluctuations in the quiet Sun

Context. The study of the dynamic properties of small-scale magnetic fields in the quiet photosphere is important for several reasons: (i) it allows us to characterise the dynamic regime of the magnetic field and points out some aspects that play a key role in turbulent convection processes; (ii) it provides details of the processes and the spatial and temporal scales in the solar photosphere at which the magnetic fields emerge, vary, and eventually decay; and (iii) it provides physical constraints on models, improving their ability to reliably represent the physical processes occurring in the quiet Sun. Aims. We aim to characterise the dynamic properties of small-scale magnetic fields in the quiet Sun through the investigation of the scaling properties of magnetic field fluctuations. Methods. To this end, we applied the structure functions analysis, which is typically used in the study of complex systems (e.g. in approaching turbulence). In particular, we evaluated the so-called Hölder-Hurst exponent, which points out the persistent nature of magnetic field fluctuations in the field of view targeted at a whole supergranule in the disc centre. Results. We present the first map of a solar network quiet region as represented by the Hölder-Hurst exponent. The supergranular boundary is characterised by persistent magnetic field fluctuations, which indicate the occurrence of longer-memory processes. On the contrary, the regions inside the supergranule are characterised by antipersistent magnetic field fluctuations, which suggest the occurrence of physical processes with a short memory. Classical Kolmogorov homogeneous and isotropic turbulence, for instance, belongs to this class of processes. The obtained results are discussed in the context of the current literature