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We study the systematic bias introduced when selecting the spectroscopicredshifts of brighter cluster galaxies to estimate the velocity dispersion ofgalaxy clusters from both simulated and observational galaxy catalogues. Weselect clusters with Ngal > 50 at five low redshift snapshots from asemi-analytic model galaxy catalogue, and from a catalogue of SDSS DR8 groupsand clusters across the redshift range 0.021<z<0.098. We employ variousselection techniques to explore whether the velocity dispersion bias is simplydue to a lack of dynamical information or is the result of an underlyingphysical process occurring in the cluster, for example, dynamical friction. Thevelocity dispersions and stacked particle velocity distributions of the parentdark matter (DM) halos are compared to the corresponding cluster dispersionsand galaxy velocity distribution. We find a clear bias between the halo and thesemi-analytic galaxy cluster velocity dispersion on the order of sigma gal /sigma DM = 0.87-0.95 and a distinct difference in the stacked galaxy and DMparticle velocity distribution. We identify a systematic underestimation of thevelocity dispersions when imposing increasing absolute I-band magnitude limits.This underestimation is enhanced when using only the brighter cluster membersfor dynamical analysis on the order of 5-35%, indicating that dynamicalfriction is a serious source of bias when using galaxy velocities as tracers ofthe underlying gravitational potential. In contrast to the literature we findthat the resulting bias is not only halo mass-dependent but that the nature ofthe dependence changes according to the galaxy selection strategy. We make arecommendation that, in the realistic case of limited availability of spectralobservations, a strictly magnitude-limited sample should be avoided to ensurean unbiased estimate of the velocity dispersion.

Brighter galaxy bias: underestimating the velocity dispersions of galaxy clusters