Cosmic web type dependence of halo clustering

We use the Millennium Simulation to show that halo clustering varies significantly with cosmic web type. Haloes are classified as node, filament, sheet and void haloes based on the eigenvalue decomposition of the velocity shear tensor. The velocity field is sampled by the peculiar velocities of a fixed number of neighbouring haloes, and spatial derivatives are computed using a kernel borrowed from smoothed particle hydrodynamics. The classification scheme is used to examine the clustering of haloes as a function of web type for haloes with masses larger than 10(11) h(-1)M(circle dot). We find that node haloes show positive bias, filament haloes show negligible bias and void and sheet haloes are antibiased independent of halo mass. Our findings suggest that the mass dependence of halo clustering is rooted in the composition of web types as a function of halo mass. The substantial fraction of node-type haloes for halo masses greater than or similar to 2 x 10(13) h(-1)M(circle dot) leads to positive bias. Filament-type haloes prevail at intermediate masses, 10(12)-10(13) h(-1)M(circle dot), resulting in unbiased clustering. The large contribution of sheettype haloes at low halo masses less than or similar to 10(12) h(-1)M(circle dot) generates antibiasing.