The universal distribution of halo interlopers in projected phase space.
  Bias in galaxy cluster concentration and velocity anisotropy?
  When clusters of galaxies are viewed in projection, one cannot avoid picking
up foreground/background interlopers (FBIs), that lie within the virial cone
(VC), but outside the virial sphere. Structural & kinematic deprojection
equations are not known for an expanding Universe, where the Hubble flow (HF)
stretches the line-of-sight (LOS) distribution of velocities. We analyze 93
mock relaxed clusters, built from a cosmological simulation. The stacked mock
cluster is well fit by an m=5 Einasto DM density profile (but only out to 1.5
virial radii [r_v]), with velocity anisotropy (VA) close to the Mamon-Lokas
model with VA radius equal to that of density slope -2. The surface density of
FBIs is nearly flat out to r_v, while their LOS velocity distribution shows a
dominant gaussian cluster-outskirts component and a flat field component. This
distribution of FBIs in projected phase space is nearly universal in mass. A
local k=2.7 sigma velocity cut returns the LOS velocity dispersion profile
(LOSVDP) expected from the NFW density and VA profiles measured in 3D. The HF
causes a shallower outer LOSVDP that cannot be well matched by the Einasto
model for any k. After this velocity cut, FBIs still account for 23% of DM
particles within the VC (close to the observed fraction of cluster galaxies
lying off the Red Sequence). The best-fit projected NFW/Einasto models
underestimate the 3D concentration by 6+/-6% (16+/-7%) after (before) the
velocity cut, unless a constant background is included in the fit. Assuming the
correct mass profile, the VA profile is well recovered from the measured
LOSVDP, with a slight bias towards more radial orbits in the outer regions.
These small biases are overshadowed by large cluster-cluster variations caused
by cosmic variance. An appendix provides an analytical approximation to the
surface density, projected mass and tangential shear profiles of the Einasto
model.
