Stacked phase-space density of galaxies around massive clusters: A theoretical framework and application to real data

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Masato Shirasaki, Eiichi Egami, Satoshi Miyazaki, Nobuhiro Okabe

We present a new theoretical framework to predict average histograms of line-of-sight velocities over pairs of galaxies and galaxy clusters. Since the histogram can be measured at different galaxy-cluster separations, this observable is commonly referred to as the stacked phase-space density. We formulate the stacked phase density based on a halo-model approach so that the model can be applied to real samples of galaxies and clusters. We examine our model by using an actual sample of massive clusters with known weak-lensing masses and spectroscopic observations of galaxies around the clusters. A simple likelihood analysis with our model enables us to infer the three-dimensional velocity dispersion of observed galaxies in massive clusters. We find the velocity bias of galaxies surrounding clusters with their masses of ∼1015h−1M⊙ to be 1.09±0.245 at the 68\% confidence level (including systematic errors associated with our model uncertainties). Our results confirm that the relation between the galaxy velocity dispersion and the host cluster mass in our sample is consistent with the prediction in dark-matter-only N-body simulations. We measure the line-of-sight velocity dispersions of 16701 galaxies around 23 clusters on scales of <6h−1Mpc with a 10\% level precision. Our measurement of the line-of-sight velocity dispersion is in good agreement with the standard ΛCDM prediction. Possible directions for improvement in the analysis are also discussed.

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