Title: Observational characterisation of large-scale transport and horizontal turbulent diffusivity in the quiet Sun

Abstract: The Sun is a magnetic star, and the only spatio-temporally resolved astrophysical system displaying turbulent MHD thermal convection. This makes it a privileged object of study to understand fluid turbulence in extreme regimes and its interactions with magnetic fields. Global analyses of high-resolution solar observations provided by the NASA Solar Dynamics Observatory can shed light on the physical processes underlying large-scale emergent phenomena such as the solar dynamo cycle. Combining a Coherent Structure Tracking reconstruction of photospheric flows, based on photometric data, and a statistical analysis of virtual passive tracers trajectories advected by these flows, we characterise one of the most important such processes, turbulent diffusion, over an unprecedentedly long monitoring period of 6 consecutive days of a significant fraction of the solar disc. We first confirm, and provide a new global view of the emergence of a remarkable dynamical pattern of Lagrangian Coherent Structures tiling the entire surface. These structures act as transport barriers on the time and spatial scale of supergranulation and, by transiently accumulating particles and magnetic fields, regulate large-scale turbulent surface diffusion. We then further statistically characterise the turbulent transport regime using two different methods, and obtain an effective horizontal turbulent diffusivity $D=2-3\times10^8~\mathrm{m}^2~\mathrm{s}^{-1}$ on the longest timescales probed. This estimate is consistent with the transport coefficients required in large-scale mean-field solar dynamo models, and is in broad agreement with the results of global simulations. Our analysis may also have implications for understanding the connections between solar-surface, coronal and solar-wind dynamics, and provides valuable lessons to characterise turbulent transport in other, unresolved turbulent astrophysical systems.