The universal distribution of halo interlopers in projected phase space. Bias in galaxy cluster concentration and velocity anisotropy?

TL;DR

This study investigates the distribution of interlopers in galaxy clusters' projected phase space, revealing a nearly universal pattern and analyzing biases in concentration and velocity anisotropy measurements due to interlopers and the Hubble flow.

Contribution

It provides a detailed analysis of interloper distributions in projected phase space using cosmological simulations and introduces an analytical approximation for the Einasto profile.

Findings

Interloper surface density is nearly flat out to the virial radius.

A velocity cut at 2.7 sigma recovers expected velocity dispersion profiles.

Including a background component improves concentration estimates in models.

Abstract

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.