and Cosmology

6. Clusters and Groups of Galaxies
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model is fitted to the most prominent lensed images
in the observation, i.e., either giant arcs or clearly recognizable
multiple images. In general, this model then
predicts further images of the source producing the arc.
Close to these predicted positions, these additional images
are then searched for, utilizing the morphology of
the light distribution and the color. If this initial model
describes the overall mass distribution quite well, such
images are found. The exact positions of the new images
provide further constraints on the lens model which
is then refined accordingly. Again, the new model will
predict further multiple image systems, and so on. By
this procedure, very detailed models can sometimes be
obtained. Since the lens properties of a cluster depend
on the distance or the redshift of the source, the redshift
of lensed sources can be predicted from the identification
of multiple image systems in clusters if a detailed
mass model is available. These predictions can then be
verified by spectroscopic analysis, and the success of
this method gives us some confidence in the accuracy
of the lens models.
Fig. 6.32. Distortions by the lens effect of an elliptical potential,
as a function of the source position. The first panel shows
the source itself. The second panel displays ten positions of
the source in the source plane (numbered from 1 to 10) relative
to the center of the lens; the solid curves show the inner
and outer caustics. The remaining panels (numbered from 1 to
10) show the inner and outer critical curves and the resulting
images of the source
profile within the radii at which arcs are found, or the
ellipticity of the mass distribution and its substructure.
Figure 6.33 shows two clusters of galaxies which
contain several arcs. For a long time, A 2218 was the
classic example of the existence of numerous arcs in
a single galaxy cluster. Then after the installation of
the ACS camera on-board HST in 2002, a spectacular
image of the cluster A 1689 was obtained in which
more than 100 arcs and multiple images were identified.
Several sections of this image are shown in Fig. 6.34.
For clusters of galaxies with such a rich inventory of
lens phenomena, very detailed mass models can be
constructed.
Such mass models have predictive power, allowing
an iterative modeling process. An initial simple mass
Results. We can summarize the most important results
of the examination of clusters using arcs and multiple
images as follows: the mass of galaxy clusters is
indeed much larger than the mass of their luminous
matter. The lensing method yields a mass which is in
very good agreement with mass estimates from the X-
ray method or from dynamical methods. However, the
core radius of clusters, i.e., the scale on which the mass
profile flattens inwards, is significantly smaller than determined
from X-ray observations. A typical value is
r c ∼ 30h −1 kpc, in contrast to ∼ 150h −1 kpc from the
X-ray method. This difference leads to a discrepancy
in the mass determination between the two methods on
scales below ∼ 200h −1 kpc. We emphasize that, at least
in principle, the mass determination based on arcs and
multiple images is substantially more accurate because
it does not require any assumptions about the symmetry
of the mass distribution, about hydrostatic equilibrium
of the X-ray gas, or about an isothermal temperature
distribution. On the other hand, the lens effect measures
the mass in cylinders because the lens equation
contains only the projected mass distribution, whereas
the X-ray method determines the mass inside spheres.
The conversion between the two methods introduces
uncertainties, in particular for clusters which deviate