The Cluster-EAGLE project: velocity bias and the velocity dispersion - mass relation of cluster galaxies

TL;DR

This study uses high-resolution simulations to analyze how galaxy selection criteria affect velocity dispersion measurements, finding stellar mass selection yields nearly unbiased estimates of cluster velocity dispersion across different redshifts.

Contribution

It demonstrates that selecting galaxies by stellar mass provides an unbiased estimate of cluster velocity dispersion, reducing velocity bias concerns in mass estimation.

Findings

Stellar mass-selected galaxies give <5% bias in velocity dispersion.

Velocity bias depends on the time galaxies spend inside clusters.

Bias is minimal across different cluster radii and redshifts.

Abstract

We use the Cluster-EAGLE simulations to explore the velocity bias introduced when using galaxies, rather than dark matter particles, to estimate the velocity dispersion of a galaxy cluster, a property known to be tightly correlated with cluster mass. The simulations consist of 30 clusters spanning a mass range $14.0 \le \log_{10}(M_{\rm 200c}/\mathrm{M_\odot}) \le 15.4$, with their sophisticated sub-grid physics modelling and high numerical resolution (sub-kpc gravitational softening) making them ideal for this purpose. We find that selecting galaxies by their total mass results in a velocity dispersion that is 5-10 per cent higher than the dark matter particles. However, selecting galaxies by their stellar mass results in an almost unbiased ($<5$ per cent) estimator of the velocity dispersion. This result holds out to $z=1.5$ and is relatively insensitive to the choice of cluster aperture, varying by less than 5 per cent between $r_{\rm 500c}$ and $r_{\rm 200m}$. We show that the velocity bias is a function of the time spent by a galaxy inside the cluster environment. Selecting galaxies by their total mass results in a larger bias because a larger fraction of objects have only recently entered the cluster and these have a velocity bias above unity. Galaxies that entered more than $4 \, \mathrm{Gyr}$ ago become progressively colder with time, as expected from dynamical friction. We conclude that velocity bias should not be a major issue when estimating cluster masses from kinematic methods.