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.
