Velocity Anisotropy and Shape Bias in the Caustic Technique

TL;DR

This study evaluates the accuracy of the caustic technique for measuring galaxy cluster masses using simulations, introducing a new calibration-free method that accounts for velocity anisotropies and concentration biases.

Contribution

We develop and test a calibration-free caustic mass estimation method that incorporates observables like velocities, projected positions, and estimated concentration and anisotropy.

Findings

3D measurements achieve <4% bias with 10-15% scatter.

Line-of-sight effects increase scatter to ~25%.

Biases in concentration and anisotropy cause small mass estimation errors.

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.