Velocity Anisotropy and Shape Bias in the Caustic Technique

Abstract

We use the Millennium Simulation to quantify the statistical accuracy and precision of the escape velocity technique for measuring cluster-sized halo masses at z~0.1. We show that in 3D, one can measure nearly unbiased (<4%) halo masses (>1.5x10^14 M_solar h^-1) with 10-15% scatter. Line-of-sight projection effects increase the scatter to ~25%, where we include the known velocity anisotropies. The classical "caustic" technique incorporates a calibration factor which is determined from N-body simulations. We derive and test a new implementation which eliminates the need for calibration and utilizes only the observables: the galaxy velocities with respect to the cluster mean v, the projected positions r_p, an estimate of the Navarro-Frenk-White (NFW) density concentration and an estimate of the velocity anisotropies, beta. We find that differences between the potential and density NFW concentrations induce a 10% bias in the caustic masses. We also find that large (100%) systematic errors in the observed ensemble average velocity anisotropies and concentrations translate to small (5%-10%) biases in the inferred masses.