The universal distribution of halo interlopers in projected phase space. Bias in galaxy cluster concentration and velocity anisotropy?
Abstract
When clusters of galaxies are viewed in projection, one cannot avoid picking up a fraction of foreground/background interlopers, that lie within the virial cone, but outside the virial sphere. Structural and kinematic deprojection equations are known for the academic case of a static Universe, but not for the real case of an expanding Universe, where the Hubble flow (HF) stretches the lineofsight distribution of velocities. Using 93 mock relaxed clusters, built from the dark matter (DM) particles of a hydrodynamical cosmological simulation, we quantify the distribution of interlopers in projected phase space (PPS), as well as the biases in the radial and kinematical structure of clusters produced by the HF. The stacked mock clusters are well fit by an m = 5 Einasto DM density profile (but only out to 1.5 virial radii), with velocity anisotropy (VA) close to the MamonŁokas model with characteristic radius equal to that of density slope 2. The surface density of interlopers is nearly flat out to the virial radius, while their velocity distribution shows a dominant Gaussian clusteroutskirts component and a flat field component. This distribution of interlopers in PPS is nearly universal, showing only small trends with cluster mass, and is quantified. A local κ = 2.7 sigma velocity cut is found to return the lineofsight velocity dispersion profile (LOSVDP) expected from the NFW density and VA profiles measured in three dimensions. The HF causes a shallower outer LOSVDP that cannot be well matched by the Einasto model for any value of κ. After this velocity cut, which removes 1 interloper out of 6, interlopers still account for 23 ± 1% of all DM particles with projected radii within the virial radius (surprisingly very similar to the observed fraction of cluster galaxies lying off the Red Sequence) and over 60% between 0.8 and 1 virial radius. The HF causes the bestfit projected NFW or m = 5 Einasto model to the stacked cluster to underestimate the true concentration measured in 3D by 6 ± 6% (16 7%) after (before) the velocity cut. These biases in concentration are reduced by over a factor two once a constant background is included in the fit. The VA profile recovered from the measured LOSVDP by assuming the correct mass profile recovers fairly well the VA measured in 3D, with a slight, marginally significant, bias towards more radial orbits in the outer regions. These small biases in the concentration and VA of the galaxy system are overshadowed by important clustertocluster fluctuations caused by cosmic variance and by the strong inefficiency caused by the limited numbers of observed galaxies in clusters. An appendix provides an analytical approximation to the surface density, projected mass and tangential shear profiles of the Einasto model. Another derives the expressions for the surface density and mass profiles of the NFW model projected on the sphere (for future kinematic modeling).
Appendices are only available in electronic form at http://www.aanda.org
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 2010
 DOI:
 10.1051/00046361/200913948
 arXiv:
 arXiv:1003.0033
 Bibcode:
 2010A&A...520A..30M
 Keywords:

 galaxies: clusters: general;
 cosmology: miscellaneous;
 dark matter;
 galaxies: halos;
 gravitational lensing:;
 weak;
 methods: numerical;
 Astrophysics  Cosmology and Extragalactic Astrophysics
 EPrint:
 Version published in A&