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

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 $14.0\le {\log }_{10}(M_{200\mathrm{c}}\mathrm{/}{\mathrm{M}}_{\odot })\le 15.4$, 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 $r_{500\mathrm{c}}$ and $r_{200\mathrm{m}}$. 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{G}\mathrm{y}\mathrm{r}$$ 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.