Constraining Cosmological Parameters using the Cluster Mass-Richness Relation

TL;DR

This paper derives and calibrates the galaxy cluster mass-richness relation from SDSS data, demonstrating its effectiveness in constraining cosmological parameters omega_m and sigma_8 with results comparable to Planck 2018.

Contribution

The study introduces a method to determine a linear mass-richness relation using a Hinge function cut, validated with simulations, and applies it to observational data for cosmological constraints.

Findings

The MRR shows a low-richness tail caused by systematics.

A richness threshold ensures a linear MRR with slope ~1.

Cosmological constraints are consistent with Planck 2018 results.

Abstract

The cluster mass-richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the mean matter density of the universe and the amplitude of fluctuations using the cluster abundance technique. We derive the MRR relation using GalWCat19, a publicly available galaxy cluster catalog we created from the Sloan Digital Sky Survey-DR13 spectroscopic dataset. The MRR shows a tail at the low-richness end. Using the Illustris-TNG and mini-Uchuu cosmological numerical simulations, we demonstrate that this tail is caused by systematical uncertainties. We show that, by means of a judicious cut, identified by the use of the Hinge function, it is possible to determine a richness threshold above which the MRR is linear i.e., where cluster mass scales with richness as logM_200 = alpha + beta logN_200. We derive the MRR and show it is consistent with both sets of simulations with a slope of beta ~ 1. We use our MRR to estimate cluster masses from the GalWCat19 catalog which we then use to set constraints on omega_m and sigma_8. Utilizing the all-member MRR, we obtain constraints of omega_m = 0.31 (+0.04-0.03) and sigma_8 = 0.82 (+0.05-0.04), and utilizing the red-member MRR, we obtain omega_m = 0.31 (+0.04-0.03) and sigma_8 = 0.81 (+0.05-0.04). Our constraints on omega_m and sigma_8 are consistent and very competitive with the Planck 2018 results.