Biases in the estimation of velocity dispersions and dynamical masses for galaxy clusters

TL;DR

This paper investigates biases in estimating galaxy cluster velocities and masses using simulations, and introduces new unbiased estimators that correct for these biases in small galaxy samples.

Contribution

The study characterizes biases in common estimators and proposes new unbiased methods for velocity dispersion and mass estimation in galaxy clusters.

Findings

New estimators effectively correct biases in small galaxy samples.

Bias correction improves accuracy of velocity dispersion measurements.

Method validated on simulated galaxy cluster data.

Abstract

Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime ($N_{gal} \leq 75$), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the $\sigma-M$ relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that they can retrieve bias-corrected values for both the mean velocity dispersion and the mean mass.