A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. (2007) and Forero-Romero et al. (2009) the new algorithm is based on the analysis of the velocity shear tensor rather than the gravitational tidal tensor. The procedure consists of the construction of the the shear tensor at each (grid) point in space and the evaluation of its three eigenvectors. A given point is classified to be either a void, sheet, filament or a knot according to the number of eigenvalues above a certain threshold, 0, 1, 2, or 3 respectively. The threshold is treated as a free parameter that defines the web. The algorithm has been applied to a dark matter only, high resolution simulation of a box of side-length 64$h^{-1}$Mpc and N = $1024^3$ particles with the framework of the WMAP5/LCDM model. The resulting velocity based cosmic web resolves structures down to <0.1$h^{-1}$Mpc scales, as opposed to the ~1$h^{-1}$Mpc scale of the tidal based web. The under-dense regions are made of extended voids bisected by planar sheets, whose density is also below the mean. The over-dense regions are vastly dominated by the linear filaments and knots. The resolution achieved by the velocity based cosmic web provides a platform for studying the formation of halos and galaxies within the framework of the cosmic web.Comment: 8 pages, 4 Figures, MNRAS Accepted 2012 June 19. Received 2012 May 10; in original form 2011 August 2

We use a 64$h^{-1}$Mpc dark matter (DM) only cosmological simulation to examine the large scale orientation of haloes and substructures with respect the cosmic web. A web classification scheme based on the velocity shear tensor is used to assign to each halo in the simulation a web type: knot, filament, sheet or void. Using $\sim10^6$ haloes that span ~3 orders of magnitude in mass the orientation of the halo's spin and the orbital angular momentum of subhaloes with respect to the eigenvectors of the shear tensor is examined. We find that the orbital angular momentum of subhaloes tends to align with the intermediate eigenvector of the velocity shear tensor for all haloes in knots, filaments and sheets. This result indicates that the kinematics of substructures located deep within the virialized regions of a halo is determined by its infall which in turn is determined by the large scale velocity shear, a surprising result given the virilaized nature of haloes. The non-random nature of subhalo accretion is thus imprinted on the angular momentum measured at z = 0. We also find that haloes' spin axis is aligned with the third eigenvector of the velocity shear tensor in filaments and sheets: the halo spin axis points along filaments and lies in the plane of cosmic sheets.Comment: 5 pages, 2 figures, MNRAS Letters in Accepte

We seek to understand the relationship between galaxy properties and their local environment, which calls for a proper formulation of the notion of environment. We analyse the GIMIC suite of cosmological hydrodynamical simulations within the framework of the cosmic web as formulated by Hoffman et al., focusing on properties of simulated DM haloes and luminous galaxies with respect to voids, sheets, filaments and knots -the four elements of the cosmic web. We find that the mass functions of haloes depend on environment, which drives other environmental dependence of galaxy formation. The web shapes the halo mass function, and through the strong dependence of the galaxy properties on the mass of their host haloes, it also shapes the galaxy-(web) environment dependence.

An open question in cosmology and the theory of structure formation is to what extent does environment affect the properties of galaxies and haloes. The present paper aims at shedding light on this problem. The paper focuses on the analysis of a dark matter only simulation and it addresses the issue of how the environment affects the abundance of haloes, which are are assigned four attributes: their virial mass, an ambient density calculated with an aperture that scales with R vir (∆ M ), a fixedaperture (∆ R ) ambient density, and a cosmic web classification (i.e. voids, sheets, filaments, and knots, as defined by the V-web algorithm). ∆ M is the mean density around a halo evaluated within a sphere of a radius of 5R vir , where R vir is the virial radius. ∆ R is the density field Gaussian smoothed with R = 4 h −1 Mpc, evaluated at the center of the halo. The main result of the paper is that the difference between haloes in different web elements stems from the difference in their mass functions, and does not depend on their adaptive-aperture ambient density. A dependence on the fixed-aperture ambient density is induced by the cross correlation between the mass of a halo and its fixed-aperture ambient density.