Weak lensing mass bias and the alignment of center proxies

Galaxy cluster masses derived from observations of weak lensing suffer from a number of biases affecting the accuracy of mass-observable relations calibrated from such observations. In particular, the choice of the cluster center plays a prominent role in biasing inferred masses. In the past, empirical miscentring distributions have been used to address this issue. Using hydro-dynamical simulations, we aim to test the accuracy of weak lensing mass bias predictions based on such miscentring distributions by comparing the results to mass biases computed directly using intra-cluster medium (ICM)-based centers from the same simulation. We construct models for fitting masses to both centered and miscentered Navarro-Frenk-White profiles of reduced shear, and model the resulting distributions of mass bias with normal and log-normal distributions. We find that the standard approach of using miscentring distributions leads to an over-estimation of cluster masses at levels of between 2\% and 6\% when compared to the analysis in which actual simulated ICM centers are used, even when the underlying miscentring distributions match in terms of the miscentring amplitude. We find that neither log-normal nor normal distributions are generally reliable for approximating the shapes of the mass bias distributions, regardless of whether a centered or miscentered radial model is used.