and Cosmology

7.5 Non-Linear Structure Evolution
Indeed, this can be expected because clusters of galaxies
contain substructure, visible in the form of the cluster
galaxies. In the upper part of Fig. 7.17, the simulation of
a cluster and its substructure is displayed. Indeed, this
mass distribution looks just like the mass distribution
expected in a cluster of galaxies, with the main cluster
halo and its distribution of member galaxies. The
lower part of Fig. 7.17 shows the simulation of a halo
with mass ∼ 2 × 10 12 M ⊙ , which corresponds to a massive
galaxy. As one can easily see, its mass distribution
shows a large number of sub-halos as well. In fact, the
two mass distributions are nearly indistinguishable, ex-
303
Fig. 7.18. Number density of sub-halos as a function of their
mass. The mass is expressed by the corresponding Keplerian
rotational velocity v c , measured in units of the corresponding
rotational velocity of the main halo. The curves show this
number density of sub-halos with rotational velocity ≥ v c for
a halo of either cluster mass or galaxy mass. The observed
numbers of sub-halos (i.e., of galaxies) in the Virgo Cluster
are plotted as open circles with error bars, and the number
of satellite galaxies of the Milky Way as filled circles. One
can see that the simulations describe the abundance of cluster
galaxies quite well, but around the Galaxy significantly fewer
satellite galaxies exist than predicted by a CDM model
Fig. 7.17. Density distribution of two simulated dark matter
halos. In the top image, the halo has a virial mass of
5 × 10 14 M ⊙ , corresponding to a cluster of galaxies. The halo
in the bottom image has a mass of 2 × 10 12 M ⊙ , representing
a massive galaxy. In both cases, the presence of substructure
in the mass distribution can be seen. It can be identified with
individual cluster galaxies in the case of the galaxy cluster.
The substructure in a galaxy can not be identified easily with
any observable source population; one may expect that these
are satellite galaxies, but observations show that these are considerably
less abundant than the substructure seen here. Apart
from the length-scale (and thus also the mass-scale), both
halos appear very similar from a qualitative point of view
cept for their scaling in the total mass. 8 The presence
of substructure over a very wide range in mass is a direct
consequence of hierarchical structure formation,
in which objects of higher mass each contain smaller
structures that have been formed earlier in the cosmic
evolution.
Whereas this substructure in clusters is easily identified
with the cluster member galaxies, the question
arises as to what the sub-halos in galaxies can possibly
correspond to. These show a broad mass spectrum, as
displayed in Fig. 7.18. Some of these sub-halos are rec-
8 The reason for this is found in the property of the power spectrum
of density fluctuations that has been discussed in Sect. 7.5.2, namely
that P(k) can be approximated by a power law over a wide range in k.
Such a power law features no characteristic scale. For this reason,
the properties of halos of high and low mass are scale-invariant, as is
clearly visible in Fig. 7.17.