The geometry of the filamentary environment of galaxy clusters

We construct a filament catalogue using an extension of the halo-based filament finder of Zhang et al. (2009), in a 250 Mpc h-1 side N-body simulation, and study the properties of filaments ending upon or in the proximity of galaxy clusters (within 10 Mpc h-1). In this region, the majority of filamentary mass, halo mass and galaxy richness centred upon the cluster tends to lie in sheets, which are not always coincident. Fixing a sheet width of 3 Mpc h-1 for definiteness, we find the sheet orientations and (connected) filamentary mass, halo mass and richness fractions relative to the surrounding sphere. Filaments usually have one or more end points outside the sheet determined by filament or halo mass or richness, with at least one having a large probability to be aligned with the perpendicular of the plane. Scatter in mock cluster mass measurements, for several observables, is often correlated with the observational direction relative to these local sheets, most often for richness and weak lensing, somewhat less for Compton decrement and least often for velocity dispersions. The long axis of the cluster also tends to lie in the sheets and its orientation relative to the line of sight also correlates with mass scatter.