Cosmic Web Type Dependence of Halo Clustering
  We use the Millennium simulation to show that halo clustering varies
significantly with cosmic web type. Halos are classified as node, filament,
sheet and void halos 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 halos and spatial derivatives are computed using a
kernel borrowed from smoothed particle hydrodynamics. The classification scheme
is used to examine the clustering of halos as a function of web type for halos
with masses larger than $10^{11}$. We find that node halos show positive bias,
filament halos show negligible bias, and void and sheet halos are anti-biased
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 halos for halo masses $\gtrsim
2\times10^{13}\,h^{-1}\rm M_\odot$ leads to positive bias. Filament type halos
prevail at intermediate masses, $10^{12} - 10^{13}\,h^{-1}\rm M_\odot$,
resulting in unbiased clustering. The large contribution of sheet type halos at
low halo masses $\lesssim 10^{12}\,h^{-1}\rm M_\odot$ generates anti-biasing.
