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We develop and test with cosmological simulations a physically motivated theory for how the interplay between gravity, pressure, cooling, and self-shielding set the redshift-dependent mass scale at which haloes can accrete intergalactic gas. This theory provides a physical explanation for the halo mass scale that can accrete unshocked intergalactic gas, which has been explained with ad hoc criteria tuned to reproduce the results of a few simulations. Furthermore, it provides an intuitive explanation for how this mass scale depends on the reionization redshift, the amplitude of the ionizing background, and the redshift. We show that accretion is inhibited on to more massive haloes than had been thought because previous studies had focused on the gas fraction of haloes rather than the instantaneous mass that can accrete gas. A halo as massive as 1011 M⊙ cannot accrete intergalactic gas at z = 0, even though typically its progenitors were able to accrete gas at higher redshifts. We describe a simple algorithm that can be implemented in semi-analytic models, and we compare the predictions of this algorithm to numerical simulations. [ABSTRACT FROM PUBLISHER]

ABSTRACT We construct a filament catalogue using an extension of the halo-based filament finder of , 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. [ABSTRACT FROM AUTHOR]