Mass selection bias in galaxy cluster peculiar velocities from the kinetic Sunyaev–Zel'dovich effect

Upcoming surveys for galaxy clusters using the Sunyaev–Zel'dovich effect are potentially sensitive enough to create a peculiar velocity catalogue. The statistics of these peculiar velocities are sensitive to cosmological parameters. We develop a method to explore parameter space using N -body simulations in order to quantify dark matter halo velocity statistics which will be useful for cluster peculiar velocity observations. We show that mass selection bias from a kinetic Sunyaev–Zel'dovich velocity catalogue forecasts rms peculiar velocities with a much more complicated  Ω_m  dependency than suggested by linear perturbation theory. In addition, we show that both two-point functions for velocities disagree with linear theory predictions out to  ∼40  h ⁻¹ Mpc  separations. A pedagogical appendix is included developing linear theory notation with respect to the two-point peculiar velocities functions.