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 $10\mathrm{Mpc}$ 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.

5 pages, 6 figure, Accepted for Publication to MNRAS-letter

References in corpus (12)

• The Fourth Data Release of the Sloan Digital Sky Survey
• The Las Campanas Redshift Survey
• Shapefinders: A new shape diagnostic for large scale structure
• Inter-cluster Filaments of Galaxies Programme: Abundance and Distribution of Filaments in the 2dFGRS Catalogue
• Large Scale Structure in the SDSS Galaxy Survey
• Large Scale Structure in the SDSS DR1 Galaxy Survey
• Voids in the LCRS versus CDM Models
• Evidence for Filamentarity in the Las Campanas Redshift Survey
• PSCz Superclusters: Detection, Shapes & Cosmological Implications
• The Size of the Longest Filaments in the Universe
• Detection of Network Structure in the Las Campanas Redshift Survey
• Exploring star formation using the filaments in the Sloan Digital Sky Survey Data Release Five (SDSS DR5)

Cited by in corpus (9)

• Exploring galaxy colour in different environments of the cosmic web with SDSS
• Galaxy interactions in filaments and sheets: effects of the large-scale structures versus the local density
• Unravelling the Cosmic Web: An analysis of the SDSS DR14 with the Local Dimension
• Relating information entropy and mass variance to measure bias and non-Gaussianity
• The maximum extent of the filaments and sheets in the cosmic web: an analysis of the SDSS DR17
• Galaxy interactions in filaments and sheets: insights from EAGLE simulations
• Statistically significant length scale of filaments as a robust measure of galaxy distribution
• A Scaling Relation of the Evolving Tidal Fields in a LCDM Cosmology
• Exploring the Cosmic Web in the Sloan Digital Sky Survey Data Release Seven using the Local Dimension