VELOCITY ANISOTROPY AND SHAPE BIAS IN THE CAUSTIC TECHNIQUE

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 three dimensions one can measure nearly unbiased (<4%) halo masses (>1.5 × 1014 M☉ 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 that is determined from N-body simulations. We derive and test a new implementation that eliminates the need for calibration and utilizes only the observables: the galaxy velocities with respect to the cluster mean v, the projected positions rp , an estimate of the Navarro-Frenk-White (NFW) density concentration, and an estimate of the velocity anisotropies β. 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.