Hierarchical inference of the relationship between concentration and mass in galaxy groups and clusters

Mass is a fundamental property of galaxy groups and clusters. In principle, 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 halo 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 ∼ 1013 M⊙. 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.