The Local Dimension: a method to quantify the Cosmic Web

Abstract

It is now well accepted that the galaxies are distributed in filaments, sheets and clusters all of which form an interconnected network known as the Cosmic Web. It is a big challenge to quantify the shapes of the interconnected structural elements that form this network. Tools like the Minkowski functionals which use global properties, though well suited for an isolated object like a single sheet or filament, are not suited for an interconnected network of such objects. We consider the Local Dimension $D$, defined through $N(R)=A R^D$, where $N(R)$ is the galaxy number count within a sphere of comoving radius $R$ centered on a particular galaxy, as a tool to locally quantify the shape in the neigbourhood of different galaxies along the Cosmic Web. We expect $D \sim 1,2$ and 3 for a galaxy located in a filament, sheet and cluster respectively. Using LCDM N-body simulations we find that it is possible to determine $D$ through a power law fit to $N(R)$ across the length-scales 2 to $10 {\rm Mpc}$ for $\sim 33 %$ of the galaxies. We have visually identified the filaments and sheets corresponding to many of the galaxies with $D \sim 1$ and 2 respectively. In several other situations the structure responsible for the $D$ value could not be visually identified, either due to its being tenuous or due to other dominating structures in the vicinity. We also show that the global distribution of the $D$ values can be used to visualize and interpret how the different structural elements are woven into the Cosmic Web.Comment: 5 pages, 6 figure, Accepted for Publication to MNRAS-lette

Green valley galaxies in the cosmic web: internal versus environmental quenching

“…The galaxies reside in different types of geometric environments in the cosmic web. We quantify the geometric environment of a galaxy using the local dimension (Sarkar & Bharadwaj 2009). The local dimension of a galaxy is simply based on the number counts of galaxies within a sphere of radius R centered around it.…”

The local environment of flat galaxies

“…We aim to investigate if the flat galaxies reside preferentially in a sparser environment compared to non-flat galaxies by determining the local dimension of the these galaxies (Sarkar & Bharadwaj 2009). We obtain the 3D spatial map of the flat galaxies and non-flat galaxies using their red-shifts.…”

Relating information entropy and mass variance to measure bias and non-Gaussianity

“…The void probability function (White 1979) provides a characterization of voidness that combine many higher moments of the distribution. Other methods to quantify the cosmic web includes the percolation analysis (Shandarin & Zeldovich 1983;Einasto et al 1984), the genus statistics (Gott, Dickinson, & Melott 1986), the minimal spanning tree (Barrow et al 1985)), the Voronoi tessellation (Icke & van de Weygaert 1987;van de Weygaert & Icke 1989), the Minkowski functionals (Mecke et al 1994;Schmalzing & Buchert 1997), the Shapefinders (Sahni, Sathyaprakash,& Shandarin 1998), the critical point statistics (Colombi, Pogosyan & Souradeep 2000), the marked point process (Stoica et al 2005), the multiscale morphology filter (Aragón-Calvo et al 2007), the skeleton formalism (Sousbie et al 2008) and the local dimension (Sarkar & Bharadwaj 2009).…”