and Cosmology

7. Cosmology II: Inhomogeneities in the Universe
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ognized in our Milky Way, namely the known satellite
galaxies like, e.g., the Magellanic Clouds. In a similar
way, the satellite galaxies of the Andromeda galaxy
may also be identified with sub-halos. However, as we
have seen in Sect. 6.1, fewer than 40 members of the
Local Group are known – whereas the numerical simulations
predict hundreds of satellite galaxies for the
Galaxy. This apparent deficit in the number of observed
sub-halos is considered to be another potential problem
of CDM models.
However, one always needs to remember that the
simulations only predict the distribution of mass, and
not that of light (which is accessible to observation).
One possibility of resolving this apparent discrepancy
centers on the interpretation that these sub-halos do in
fact exist, but that most of them do not, or only weakly,
emit radiation. What appears as a cheap excuse at first
sight is indeed already part of the models of the formation
and evolution of galaxies. As will be discussed in
Sect. 9.6.3 in more detail, it is difficult to form a considerable
stellar population in halos of masses below
∼ 10 9 M ⊙ . Most halos below this mass threshold will
therefore be hardly detectable because of their low luminosity.
In this picture, sub-halos in galaxies would in
fact be present, as predicted by the CDM models, but
most of these would be “dark”.
Evidence for the Presence of CDM Substructure in
Galaxies. A direct indication of the presence of substructure
in the mass distribution of galaxies indeed
exists, which originates from gravitational lens systems.
As we have seen in Sect. 3.8, the image configuration of
multiple quasars can be described by simple mass models
for the gravitational lens. Concentrating on those
systems with four images of a source, for which the position
of the lens is also observed (e.g., with the HST),
a simple mass model for the lens has fewer free parameters
than the coordinates of the observed quasar
images that need to be fitted. Despite of this, it is possible,
with very few exceptions, to describe the angular
positions of the images with such a model very accurately.
This result is not trivial, because for some
lens systems which were observed using VLBI techniques,
the image positions are known with a precision
of better than 10 −4 arcsec, with an image separation
of the order of 1 ′′ . This result demonstrates that the
mass distribution of lens galaxies is, on scales of the
image separation, quite well described by simple mass
models.
Besides the image positions, such lens models also
predict the magnifications μ of the individual images.
Therefore, the ratio of the magnifications of two images
should agree with the flux ratio of these images
of the background source. The surprising result from
the analysis of lens systems is that, although the image
positions of (nearly) all quadruply imaged systems are
very precisely reproduced by a simple mass model, in
not a single one of these systems does the mass model
reproduce the flux ratios of the images!
Perhaps the simplest explanation for these results is
that the simple mass models used for the lens are not
correct and other kinds of lens models should be used.
However, this explanation can be excluded for many of
the observed systems. Some of these systems contain
Fig. 7.19. 8.5-GHz map of the lens system 2045+265. The
source at z s = 1.28 is imaged four-fold (components A-D) by
a lens galaxy at z s = 0.867, while component E represents
emission from the lens, as is evident from its different radio
spectrum. From the general properties of the gravitational lens
mapping, one can show that any “smooth” mass model of the
lens predicts the flux of B to be roughly the same as the sum
of the fluxes of components A and C. Obviously, this rule is
strongly violated in this lens system, because B is weaker than
both A and C. This result can only be explained by small-scale
structure in the mass distribution of the lens galaxy