We study the systematic bias introduced when selecting the spectroscopic redshifts of brighter cluster galaxies to estimate the velocity dispersion of galaxy clusters from both simulated and observational galaxy catalogues .
We select clusters with N _ { gal } \geq 50 at five low redshift snapshots from the publicly available De Lucia & Blaziot semi-analytic model galaxy catalogue .
Clusters are also selected from the Tempel SDSS DR8 groups and clusters catalogue across the redshift range 0.021 \leq z \leq 0.098 .
We employ various selection techniques to explore whether the velocity dispersion bias is simply due to a lack of dynamical information or is the result of an underlying physical process occurring in the cluster , for example , dynamical friction experienced by the brighter cluster members .
The velocity dispersions of the parent dark matter ( DM ) halos are compared to the galaxy cluster dispersions and the stacked distribution of DM particle velocities are examined alongside the corresponding galaxy velocity distribution .
We find a clear bias between the halo and the semi-analytic galaxy cluster velocity dispersion on the order of \sigma _ { gal } / \sigma _ { DM } \sim 0.87 - 0.95 and a distinct difference in the stacked galaxy and DM particle velocities distribution .
We identify a systematic underestimation of the velocity dispersions when imposing increasing absolute I-band magnitude limits .
This underestimation is enhanced when using only the brighter cluster members for dynamical analysis on the order of 5 - 35 \% , indicating that dynamical friction is a serious source of bias when using galaxy velocities as tracers of the underlying gravitational potential .
In contrast to the literature we find that the resulting bias is not only halo mass-dependent but that the nature of the dependence changes according to the galaxy selection strategy .
We make a recommendation that , in the realistic case of limited availability of spectral observations , a strictly magnitude-limited sample should be avoided to ensure an unbiased estimate of the velocity dispersion .