Exploring the Cosmic Web in the Sloan Digital Sky Survey Data Release Seven using the Local Dimension

It is possible to visualize the Cosmic Web as an interconnected network of one-dimensional filaments, two-dimensional sheets and three-dimensional volume-filling structures which we refer to as clusters. We have used the Local Dimension D, which takes values D = 1, 2 and 3 for filaments, sheets and clusters, respectively, to analyse the Cosmic Web in a three-dimensional volume-limited galaxy sample from the Sloan Digital Sky Survey Data Release 7. The analysis was carried out separately using three different ranges of length-scales: 0.5-5, 1-10 and 5-50 $h^{-1} {\rm Mpc}$. We find that there is a progressive increase in the D values as we move to larger length-scales. At the smallest length-scale, the galaxies predominantly reside in filaments and sheets. There is a shift from filaments to sheets and clusters at larger scales. Filaments are completely absent at the largest length-scale (5-50 $h^{-1} {\rm Mpc}$). Considering the effect of the density environment on the Cosmic Web, we find that the filaments preferentially inhabit regions with a lower density environment as compared to sheets and clusters which prefer relatively higher density environments. A similar length-scale dependence and environment dependence was also found in a galaxy sample drawn from the Millennium Simulation which was analysed in exactly the same way as the actual data.