Quantifying the Projected Suppression of Cluster Escape Velocity
  Profiles
  The 3D 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 3D 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 undersampling of the
phase spaces and that the 3D radial escape edge can be accurately inferred from
projected data. We build an analytical model for this suppression that only
requires the number of observed galaxies $N$ in the phase-space data within the
sky-projected range $0.3 \le r_\perp/R_{200, \text{critical}} \le 1$. The
radially averaged suppression function is an inverse power law $\langle
Z_\text{v} \rangle = 1 + (N_0/N)^\lambda$ with $N_0 = 17.818$ and $\lambda=
0.362$. We test our model with $N$-body simulations, using dark matter
particles, subhalos, and semianalytic galaxies as the phase-space tracers, and
find excellent agreement. We also assess the model for systematic biases from
cosmology ($\Omega_{\Lambda}$, $H_0$), cluster mass ($M_{200,
\text{critical}}$), and velocity anisotropy ($\beta$). We find that varying
these parameters over large ranges can impart a maximal additional fractional
change in $\langle Z_\text{v} \rangle$ of $2.7\%$. These systematics are highly
subdominant (by at least a factor of 13.7) to the suppression from $N$.
