In the last few decades, the dynamic properties of the quiet Sun have been thoroughly investigated using a range of substantially different techniques, allowing us to elaborate a consistent picture of the photospheric dynamics by approaching the problem from different points of view. Particularly interesting and promising are the studies involving the tracking of small-scale magnetic fields in the quiet photosphere. Such investigations reveal features that still cannot be captured by theoretical models and/or simulations because of the complexity of the system and the simultaneous coupling of a wide range of spatial and temporal scales. These studies are based on the hypothesis that magnetic fields are passively transported by the plasma flow and provide a characterisation of advection and diffusion processes in the quiet photosphere from granular to supergranular scales (see, e.g. Wang 1988; Berger et al. 1998; Cadavid et al. 1998, 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Sánchez Almeida et al. 2010; Abramenko et al. 2011; Manso Sainz et al. 2011; Lepreti et al. 2012; Giannattasio et al. 2013, 2014a,b; Giannattasio et al. 2019; Keys et al. 2014; Caroli et al. 2015; Del Moro et al. 2015; Yang et al. 2015a,b; Roudier et al. 2016; Abramenko 2017; Kutsenko et al. 2018; Agrawal et al. 2018; Giannattasio & Consolini 2021). These studies reveal an anomalous scaling of magnetic field transport with a superdiffusive character consistent with a Levy walk inside supergranules and a more Brownian-like motion in their boundary. This has provided constraints on the magnetic flux emergence and evolution that models have to consider in order to fully explain the dynamics governing these environments. At the same time, the scaling laws affecting magnetic fields in the quiet Sun are crucial to understanding how such fields vary with scale size, despite the small scales at which dissipation occurs still being inaccessible with the currently available observations (see, e.g. Lawrence et al. 1994; Stenflo 2012, and references therein). For example, in the milestone work by Stenflo (2012), the spectrum of magnetic flux density in the quiet Sun was found to be consistent with a Kolmogorov power-law scaling. The scale at which scale invariance is broken lies below the current resolution limit. This latter author argued that the collapse of magnetic fields in Kilogauss flux tubes injects energy that is expected to cascade down because of the flux decay occurring via interchange instability, and to fragment into weaker ‘hidden’ fields at smaller scales (down to ∼10 km). As far as we know, no other studies have focused on the scaling properties characterising the magnetic fields in a quiet Sun region within a range of spatial and temporal scales from (sub)granular to supergranular in the time domain. In this work, for the first time we apply the structure function analysis typical of complex systems (Frisch 1995) to fill this gap. This approach complements the studies based on feature tracking mentioned above. The main difference is that, while in those works statistical properties of the photospheric plasma flows are investigated via the transport of small-scale magnetic fields in a frozen-in condition, here we directly study the magnetic field variations emerging from magnetogram time-series. The paper is organised as follows. Section 2 describes the data set used and the analysis techniques applied. Section 3 describes the obtained results, while Sect. 4 is devoted to their discussion in the light of current literature. Finally, in Sect. 5, we present our conclusions and present future perspectives.
Citation: Giannattasio et al. 2013
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Citation: Kutsenko et al. 2018
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