[Paper Review] A geometrical model for the catalogs of galaxies

Lorenzo Zaninetti|arXiv (Cornell University)|Mar 3, 2010

Scientific Research and Discoveries9 references3 citations

TL;DR

This paper proposes a 3D Voronoi tessellation model based on irregular Poissonian point processes to simulate the spatial distribution of galaxies in large-scale surveys. By modeling galaxy counts as a function of redshift and magnitude using photometric constraints and Voronoi face intersections, the model successfully reproduces the correlation function, void structures (including the Eridanus super-void), and observed catalog slices from the 2dFGRS and RC3, with statistical validation via maximum likelihood estimation of redshift critical parameters.

ABSTRACT

The 3D network originated by the faces of irregular Poissonian Voronoi Polyhedrons may represent the backbone on which the galaxies are originated. As a consequence the spatial appearance of the catalogs of galaxies can be reproduced. The selected catalogs to simulate are the 2dF Galaxy Redshift Survey and the Third Reference Catalog of Bright Galaxies. In order to explain the number of observed galaxies for a given flux/magnitude as a function of the redshift, the photometric properties of the galaxies should be carefully examined from both the astronomical and theoretical point of view. The statistics of the Voronoi normalized volume is modeled by two distributions and the Eridanus super-void is identified as the largest volume belonging to the Voronoi Polyhedron. The behavior of the correlation function for galaxies is simulated by adopting the framework of thick faces of Voronoi Polyhedrons on short scales, while adopting standard arguments on large scales.

Motivation & Objective

• To develop a geometrical model that reproduces the observed spatial distribution of galaxies in large-scale catalogs such as the 2dF Galaxy Redshift Survey and the Third Reference Catalog of Bright Galaxies.
• To address the lack of detailed 3D redshift-dependent displacement and photometric information in existing N-body, dynamical, and halo models.
• To simulate the number of observed galaxies per flux/magnitude as a function of redshift using photometric properties and Voronoi geometry.
• To model the appearance of voids and large-scale structures, including the Eridanus super-void, via the normalized volume distribution of Voronoi polyhedra.
• To validate the model by comparing simulated correlation functions and catalog slices with real astronomical data.

Proposed method

• The model uses a 3D network of faces from irregular Poissonian Voronoi polyhedra as a backbone for galaxy placement.
• Galaxy counts per redshift and magnitude are simulated by combining photometric luminosity functions (e.g., Schechter function) with the intersection of radial slices and Voronoi faces.
• The correlation function is modeled using the concept of 'thick faces' of Voronoi polyhedra on small scales (0–10 Mpc/h), while large-scale behavior is modeled using standard cosmological arguments.
• The maximum likelihood estimator (MLE) is applied to derive critical redshift parameters, with equations derived for both the Schechter luminosity function and the M–L relationship.
• Spherical cuts at increasing redshifts simulate all-sky catalogs like RC3, with the Zone of Avoidance incorporated via theoretical modeling.
• The model uses the normalized volume distribution of Voronoi cells to identify and characterize voids, including the Eridanus super-void as the largest such volume.

Experimental results

Research questions

• RQ1 Can the theoretical number of galaxies per flux/magnitude be accurately matched to observations as a function of redshift using a Voronoi-based model?
• RQ2 How does the Malmquist bias affect the comparison between theoretical and observed galaxy counts versus redshift?
• RQ3 Can an algorithm be developed to model the intersection between a radial slice from the observer's position and the faces of irregular Voronoi polyhedra?
• RQ4 Does the Voronoi model reproduce the observed slices of galaxies in surveys such as the 2dFGRS?
• RQ5 Can voids in all-sky surveys like RC3 be explained through the distribution of normalized Voronoi cell volumes?

Key findings

• The model successfully reproduces the two-point correlation function of galaxies on both small scales (0–10 Mpc/h) and large scales (40–200 Mpc/h), with minimal deviation from observed data in the 2dFGRS simulation.
• The Eridanus super-void is identified as the largest normalized volume within the Voronoi polyhedra, confirming its significance in the simulated structure.
• The simulated 2dFGRS catalog slices and RC3-like all-sky distributions match the observed data, including the influence of the Zone of Avoidance.
• The minimum in the large-scale correlation function is attributed to the combined effect of voids and photometric redshift behavior, supporting the hypothesis that voids are responsible for this feature.
• The maximum likelihood estimator successfully derives the critical redshift parameter $\widehat{z}_{crit}$, with closed-form solutions for both the Schechter function and M–L relationship.
• The model predicts the probability of supervoids given an average void diameter, and it captures acoustic oscillations in the correlation function at approximately 100 Mpc/h in simulated Voronoi slices.