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The Redshift-Space Cluster-Galaxy Cross-Correlation Function: I. Modeling Galaxy Infall onto Millennium Simulation Clusters and SDSS Groups

The large scale infall of galaxies around massive clusters provides a potentially powerful diagnostic of structure growth, dark energy, and cosmological deviations from General Relativity. We develop and test a method to recover galaxy infall kinematics (GIK) from measurements of the redshift-space cluster-galaxy cross-correlation function ξ_{cg}(r_p,r_π). Using galaxy and halo samples from the Millennium simulation, we calibrate an analytic model of the galaxy kinematic profiles comprised of a virialized component with an isotropic Gaussian velocity distribution and an infall component described by a skewed 2D t-distribution with a characteristic infall velocity v_r and separate radial and tangential dispersions. We show that convolving the real-space cross-correlation function with this velocity distribution accurately predicts the redshift-space ξ_{cg}, and we show that measurements of ξ_{cg} can be inverted to recover the four distinct elements of the GIK profiles. These in turn provide diagnostics of cluster mass profiles, and we expect the characteristic infall velocity v_r(r) in particular to be insensitive to galaxy formation physics that can affect velocity dispersions within halos. As a proof of concept we measure ξ_{cg} for rich galaxy groups in the Sloan Digital Sky Survey and recover GIK profiles for groups in two bins of central galaxy stellar mass. The higher mass bin has a v_r(r) curve very similar to that of 10^{14} Msun halos in the Millennium simulation, and the recovered kinematics follow the expected trends with mass. GIK modeling of cluster-galaxy cross-correlations can be a valuable complement to stacked weak lensing analyses, allowing novel tests of modified gravity theories that seek to explain cosmic acceleration.