Issue |
A&A
Volume 520, September-October 2010
|
|
---|---|---|
Article Number | A30 | |
Number of page(s) | 22 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361/200913948 | |
Published online | 24 September 2010 |
The universal distribution of halo interlopers in projected phase space*
Bias in galaxy cluster concentration and velocity anisotropy?
1
Institut d'Astrophysique de Paris (UMR 7095: CNRS & UPMC), 98 bis
Bd. Arago, 75014 Paris, France e-mail: gam@iap.fr
2
Astrophysics & BIPAC, University of Oxford, Keble Rd, Oxford OX13RH, UK
3
INAF, Osservatorio Astronomico di Trieste, Trieste, Italy
4
INAF, Osservatorio Astronomico di Torino, Torino, Italy
Received:
22
December
2009
Accepted:
1
July
2010
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 line-of-sight 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 Mamon-Łokas
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 cluster-outskirts
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 line-of-sight 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 best-fit projected NFW or m = 5 Einasto model to the
stacked cluster to underestimate the true concentration measured in 3D by
6 ± 6% (16 ) 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 cluster-to-cluster
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).
Key words: galaxies: clusters: general / cosmology: miscellaneous / dark matter / galaxies: halos / gravitational lensing: weak / methods: numerical
Appendices are only available in electronic form at http://www.aanda.org
© ESO, 2010
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