The effect of selection -- a tale of cluster mass measurement bias induced by correlation and projection

Cosmology analyses using galaxy clusters by the Dark Energy Survey have recently uncovered an issue of previously unknown selection effect affecting weak lensing mass estimates. In this letter, we use the Illustris-TNG simulation to demonstrate that selecting on galaxy counts induces a selection effect because of projection and correlation between different observables. We compute the weak-lensing-like projected mass estimations of dark matter halos and examine their projected subhalo counts. In the 2-D projected space, halos that are measured as more massive than truth have higher subhalo counts. Thus, projection along the line of sight creates cluster observables that are correlated with cluster mass measurement deviations, which in turn creates a mass measurement bias when the clusters are selected by this correlated observable. We demonstrate that the bias is predicted in a forward model using the observable-mass measurement correlation.