Hierarchical inference of the relationship between Concentration and Mass in Galaxy Groups and Clusters

TL;DR

This paper introduces a hierarchical model to infer the relationship between mass and concentration in galaxy groups and clusters, improving parameter estimation from noisy data and enabling predictions for future observations.

Contribution

The authors develop a hierarchical inference method for mass and concentration, addressing degeneracies and enabling population-level insights from low signal-to-noise measurements.

Findings

The hierarchical model accurately recovers mass-concentration relations from toy data.

Application to real data reveals the population's concentration-mass-redshift relationship.

Stacking methods can bias mass and concentration estimates depending on the approach.

Abstract

Mass is a fundamental property of galaxy groups and clusters. In theory weak gravitational lensing will enable an approximately unbiased measurement of mass, but parametric methods for extracting cluster masses from data require the additional knowledge of concentration. Measurements of both mass and concentration are limited by the degeneracy between the two parameters, particularly in low mass, high redshift systems where the signal-to-noise is low. In this paper we develop a hierarchical model of mass and concentration for mass inference we test our method on toy data and then apply it to a sample of galaxy groups and poor clusters down to masses of $\sim$ 1e13 M$_\odot$. Our fit and model gives a relationship among masses, concentrations and redshift that allow prediction of these parameters from incomplete and noisy future measurements. Additionally the underlying population can be used to infer an observationally based concentration-mass relation. Our method is equivalent to a quasi- stacking approach with the degree of stacking set by the data. We also demonstrate that mass and concentration derived from pure stacking can be offset from the population mean with differing values depending on the method of stacking.