and Cosmology

8.2 Cosmological Parameters from Clusters of Galaxies
Fig. 8.10. An optical image taken in the direction of the Great
Attractor. This image has a side length of half a degree and
was observed by the WFI at the ESO/MPG 2.2-m telescope
on La Silla. The direction of this pointing is only ∼ 7 ◦ away
from the Galactic disk. For this reason, the stellar density in
the image is extremely high (about 200 000 stars can be found
in this image) and, due to extinction in the disk of the Milky
Way, much fewer faint galaxies at high redshift are found
in this image than in comparable images at high Galactic
latitude. Nevertheless, a large number of galaxies are visible
(greenish), belonging to a huge cluster of galaxies (ACO 3627,
at a distance of about 80 Mpc), which is presumably the main
contributor to the Great Attractor
culiar velocity u(x) which we can specialize to the point
of origin x = 0. This relation is based on the assumption
of linear biasing. A galaxy at distance D contributes to
the peculiar velocity by an amount ∝ m/D 2 , where m
is its mass. If we assume that the mass-to-light ratio of
galaxies are all the same, then m ∝ L and the contribution
of this galaxy to u is ∝ L/D 2 ∝ S. Hence, under
these simplifying assumptions the contribution of a galaxy
to the peculiar velocity depends only on its observed
flux.
To apply this simple idea to real data, we need an
all-sky map of the galaxy distribution. This is difficult
to obtain, due to the presence of extinction towards the
Galactic plane. However, if the galaxy distribution is
mapped at infrared wavelengths, these effects are minimized.
It is therefore not surprising that most of the
studies on the dipole distribution of galaxies concentrate
on infrared surveys. The IRAS source catalog still
provides one of the major catalogs for such an analysis.
More recently, the Two-Micron All Sky Survey
(2MASS) catalog provided an all-sky map in the near-IR
which can be used as well. The NIR also has the advantage
that the luminosity at these wavelengths traces
the mass of the stellar population of a galaxy quite well,
in contrast to shorter wavelength for which the massto-light
ratio among galaxies varies much more. The
results of these studies is that the dipole of the galaxy
distribution lies within ∼ 20 ◦ of the CMB dipole. This
is quite a satisfactory result, if we consider the number
of assumptions that are made in this method. The amplitude
of the expected velocity depends on the factor
β = Ωm 0.6 /b. Thus, by comparing the predicted velocity
from the galaxy distribution with the observed dipole
of the CMB this factor can be determined, yielding
β = 0.49 ± 0.04.
Supplementing the photometric surveys with redshifts
allows the determination of the distance out to
which the galaxy distribution has a marked effect on
the Local Group velocity, by adding up the contributions
of galaxies within a maximum distance from the
Local Group. Although the detailed results from different
groups vary slightly, the characteristic distance turns
out to be ∼ 150h −1 Mpc, i.e., larger than the distance to
the putative Great Attractor. In fact, earlier results suggested
a considerably smaller distance, which was one
of the reasons for postulating the presence of the Great
Attractor.
8.2 Cosmological Parameters
from Clusters of Galaxies
Being the most massive and largest gravitationally
bound and relaxed objects in the Universe, clusters
of galaxies are of special value for cosmology.
In this section, we will explain various methods by
which cosmological parameters have been derived from
observations of galaxy clusters.
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