and Cosmology

6.5 Clusters of Galaxies as Gravitational Lenses
width is unresolved even by the HST, indicating an extreme
length-to-width ratio. For many arcs, additional
images of the same source were discovered, sometimes
called “counter arcs”. The identification of multiple
images is performed either by optical spectroscopy
(which is difficult in general, because one arc is highly
magnified while the other images of the same source
are considerably less strongly magnified and therefore
much fainter in general, and also because spectroscopy
of faint sources is very time-consuming), by multicolor
photometry (all images of the same source should
have the same color), or by common morphological
properties.
261
Fig. 6.31. The cluster of galaxies Cl 2244−02 at redshift
z = 0.33 is the second cluster in which an arc was discovered.
Spectroscopic analysis of this arc revealed the redshift
of the corresponding source to be z s = 2.24 – at the time of
discovery in 1987, it was the first normal galaxy detected at
aredshift> 2. This image was observed with the near-IR camera
ISAAC at the VLT. Above the arc, one can see another
strongly elongated source which is probably associated with
a galaxy at very high redshift as well
tion of clusters, derived from X-ray observations before
ROSAT, it was estimated that the central surface mass
density of clusters is not sufficiently high for strong
effects of gravitational light deflection to occur. This
incorrect estimate of the central surface mass density
in clusters originated from analyses utilizing the β-
model which, as briefly discussed above, starts with
some heavily simplifying assumptions. 6
Hence, arcs are strongly distorted and highly magnified
images of galaxies at high redshift. In some massive
clusters several arcs were discovered and the unique angular
resolution of the HST played a crucial role in such
observations. Some of these arcs are so thin that their
6 Another lesson that can be learned from the discovery of the arcs
is one regarding the psychology of researchers. After the first observations
of arcs were published, several astronomers took a second
look at their own images of these two clusters and clearly detected
the arcs in them. The reason why this phenomenon, which had been
observed much earlier, was not published before can be explained
by the fact that researchers were not completely sure about whether
these sources were real. A certain tendency prevails in not recognizing
phenomena that occur unexpectedly in data as readily as results
which are expected. However, there are also those researchers who
behave in exactly the opposite manner and even interpret phenomena
expected from theory in some unusual way.
Lens Models. Once again, the simplest mass model
for a galaxy cluster as a lens is the singular isothermal
sphere (SIS). This lens model was discussed previously
in Sect. 3.8.2. Its characteristic angular scale is specified
by the Einstein radius (3.60), or
θ E = 28 ′′ . 8
σ
) (
v
2 Dds
1000 km/s
(
)
. (6.56)
D s
Very high magnifications and distortions of images can
occur only very close to the Einstein radius. This immediately
yields an initial mass estimate of a cluster, by
assuming that the Einstein radius is about the same as the
angular separation of the arc from the center of the cluster.
The projected mass within the Einstein radius can
then be derived, using (3.66). Since clusters of galaxies
are, in general, not spherically symmetric and may show
significant substructure, so that the separation of the arc
from the cluster’s center may deviate significantly from
the Einstein radius, this mass estimate is not very accurate
in general; the uncertainty is estimated to be ∼ 30%.
Models with asymmetric mass distributions predict a variety
of possible morphologies for the arcs and the positions
of multiple images, as is demonstrated in Fig. 6.32
for an elliptical lens. If several arcs are discovered in
a cluster, or several images of the source of an arc, we
can investigate detailed mass models for such a cluster.
The accuracy of these models depends on the number
and positions of the observed lensed images; e.g., on
how many arcs and how many multiple image systems
are available for modeling. The resulting mass models
are not unambiguous, but they are robust. Clusters that
contain many lensed images have very well-determined
mass properties, for instance the mass and the mass