Toward Unbiased Galaxy Cluster Masses from Line of Sight Velocity Dispersions

We study the use of red sequence selected galaxy spectroscopy for unbiased estimation of galaxy cluster masses. We use the publicly available galaxy catalog produced using the semi-analytic model of De Lucia & Blaizot (2007) on the Millenium Simulation (Springel et al. 2005). We make mock observations to mimic the selection of the galaxy sample, the interloper rejection and the dispersion measurements for large numbers of simulated clusters spanning a wide range in mass and redshift. We explore the impacts on selection using galaxy color, projected separation from the cluster center, and galaxy luminosity. We probe for biases and characterize sources of scatter in the relationship between cluster virial mass and velocity dispersion. We identify and characterize the following sources of bias and scatter: intrinsic properties of halos in the form of halo triaxiality, dynamical friction of red luminous galaxies and interlopers. We show that due to halo triaxiality the intrinsic scatter of estimated line-of-sight dynamical mass is about three times larger (30 − 40%) than the one estimated using the 3D velocity dispersion (∼ 12%) and a small bias (. 1%) is induced. Furthermore we find evidence of increasing scatter as a function of redshift and provide a fitting formula to account for it. We characterize the amount of bias and scatter introduced by dynamical friction when using subsamples of red-luminous galaxies to estimate the velocity dispersion. We study the presence of interlopers in spectroscopic samples and their effect on the estimated cluster dynamical mass. Our results show that while cluster velocity dispersions extracted from a few dozen red sequence selected galaxies do not provide precise masses on a single cluster basis, an ensemble of cluster velocity dispersions can be combined to produce a precise calibration of a cluster survey mass–observable relation. Currently, disagreements in the literature on simulated subhalo velocity dispersionmass relations place a systematic floor on velocity dispersion mass calibration at the 15% level in mass. We show that the selection related uncertainties are small by comparison, providing hope that with further improvements to numerical studies this systematic floor can be substantially reduced.