Internal properties and environments of dark matter haloes

We use seven high-resolution N-body simulations to study the correlations among different halo properties (assembly time, spin, shape and substructure), and how these halo properties are correlated with the large-scale environment in which haloes reside. The large-scale tidal field estimated from haloes above a mass threshold is used as our primary quantity to characterize the large-scale environment, while other parameters, such as the local overdensity and the morphology of large-scale structure, are used for comparison. For haloes at a fixed mass, all the halo properties depend significantly on environment, particularly the tidal field. The environmental dependence of halo assembly time is primarily driven by local tidal field. The mass of the unbound fraction in substructure is boosted in strong tidal force region, while the bound fraction is suppressed. Haloes have a tendency to spin faster in a stronger tidal field and the trend is stronger for more massive haloes. The spin vectors show significant alignment with the intermediate axis of the tidal field, as expected from the tidal torque theory. Both the major and minor axes of haloes are strongly aligned with the corresponding principal axes of the tidal field. In general, a halo that can accrete more material after the formation of its main halo on average is younger, more elongated, spins faster and contains a larger amount of substructure. Higher-density environments not only provide more material for haloes to accrete, but also are places of stronger tidal fields that tend to suppress halo accretion. The environmental dependencies are the results of these two competing effects. The tidal field based on haloes can be estimated from observation, and we discuss the implications of our results for the environmental dependence of galaxy properties.