Quantifying the Projected Suppression of Cluster Escape Velocity Profiles

The radial escape-velocity profile of galaxy clusters has been suggested to be a promising and competitive tool for constraining mass profiles and cosmological parameters in an accelerating universe. However, the observed line-of-sight escape profile is known to be suppressed compared to the underlying radial (or tangential) escape profile. Past work has suggested that velocity anisotropy in the phase-space data is the root cause. Instead we find that the observed suppression is from the statistical under-sampling of the phase-spaces and that the radial escape edge can be accurately inferred from projected data. We build an analytical model for this suppression which only requires the number of observed galaxies $N$ in the phase-space data within the sky-projected range $0.3 \le r/R_{200,critical} \le 1$. The suppression function is an inverse power-law $Z_v = 1 + (N_0/N)^\lambda$ with $N_0 = 14.205$ and $\lambda= 0.467$. We test our model with N-body simulations, using dark matter particles, sub-halos, and semi-analytic galaxies as the phase-space tracers and find percent level accuracy and precision. We show that this suppression function is independent of cluster mass, cosmology, and velocity anisotropy.