Topological Approach to Void Finding Applied to the SDSS Galaxy Map.

Area of Science:

• Cosmology
• Astrophysics
• Data Analysis

Background:

• The large-scale structure of the low-redshift Universe is characterized by a multiscale distribution of cosmic voids, separated by filaments and walls of galaxies.
• Cosmic voids serve as crucial cosmological probes, but their physical properties are challenging to ascertain due to observational limitations like shot noise and sparse tracer particles.

Purpose of the Study:

• To develop and apply a robust, topology-based void-finding algorithm using Persistent Homology.
• To analyze the properties of cosmic voids in the Sloan Digital Sky Survey (SDSS) I/II Main Galaxy Catalog and compare them with mock cosmological simulations.

Main Methods:

• Utilized Persistent Homology, a topology-based approach, to identify persistent features in galaxy distribution data.
• Applied the algorithm to a volume-limited subsample of SDSS galaxies (M_r < -20.19) and Horizon Run 4 cosmological N-body simulations.
• Measured void size distribution, radial density profiles, sphericity, and nearest neighbor separations.

Main Results:

• Identified 32 topologically robust voids in the SDSS data within the redshift range of 0.02 to 0.116.
• Void effective radii ranged from 21 to 56 h^-1 Mpc.
• The median nearest neighbor separation between voids was approximately 57 h^-1 Mpc, and the median radial profile matched simulations.

Conclusions:

• The developed Persistent Homology void-finding algorithm provides a robust method for characterizing cosmic voids.
• The measured properties of voids in the SDSS data are consistent with expectations from cosmological simulations, validating the method.
• This approach enhances our ability to use cosmic voids as cosmological probes.