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Mapping and characterisation of cosmic filaments in galaxy cluster outskirts: strategies and forecasts for observations from simulations

Upcoming wide-field surveys are well-suited to studying the growth of galaxy clusters by tracing galaxy and gas accretion along cosmic filaments. We use hydrodynamic simulations of volumes surrounding 324 clusters from \textsc{The ThreeHundred} project to develop a framework for identifying and characterising these filamentary structures, and associating galaxies with them. We define 3-dimensional reference filament networks reaching $5R_{200}$ based on the underlying gas distribution and quantify their recovery using mock galaxy samples mimicking observations such as those of the WEAVE Wide-Field Cluster Survey. Since massive galaxies trace filaments, they are best recovered by mass-weighting galaxies or imposing a bright limit (e.g. $>L^*$) on their selection. We measure the transverse gas density profile of filaments, derive a characteristic filament radius of $\simeq0.7$--$1~h^{-1}\rm{Mpc}$, and use this to assign galaxies to filaments. For different filament extraction methods we find that at $R>R_{200}$, $\sim15$--$20%$ of galaxies with $M_*>3 \times 10^9 M_{\odot}$ are in filaments, increasing to $\sim60%$ for galaxies more massive than the Milky-Way. The fraction of galaxies in filaments is independent of cluster mass and dynamical state, and is a function of cluster-centric distance, increasing from $\sim13$% at $5R_{200}$ to $\sim21$% at $1.5R_{200}$. As a bridge to the design of observational studies, we measure the purity and completeness of different filament galaxy selection strategies. Encouragingly, the overall 3-dimensional filament networks and $\sim67$% of the galaxies associated with them are recovered from 2-dimensional galaxy positions.