The redshift-space cluster-galaxy cross-correlation function - I. Modelling galaxy infall on to 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 xi(s)(cg)(r(p), r(pi)). Using galaxy and halo samples from the Millennium simulation, we calibrate an analytic model of the galaxy kinematic profiles comprising 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, c) 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 xi(s)(cg), and we show that measurements of xi(s)(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, c)(r) in particular to be insensitive to galaxy formation physics that can affect velocity dispersions within haloes. As a proof of concept we measure xi(s)(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, c)(r) curve very similar to that of 10(14) h(-1) M-circle dot haloes in the Millennium simulation, and the recovered kinematics follow the expected trends with mass. GIK modelling 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.