Clusters of galaxies are the largest gravitationally bound
systems known to be in quasi-equilibrium. This allows for
reliable estimates to be made of their mass as well as their
dynamical and thermal attributes. The richest clusters, arising
from 3
density fluctuations, can be as massive as
solar masses, and the environment in these structures is
composed of shock heated gas with temperatures of order
degrees Kelvin which emits thermal bremsstrahlung and line
radiation at X-ray energies. Also, because of their spatial size
Mpc and separations of order
Mpc, they provide a measure of nonlinearity on scales close to
the perturbation normalization scale
Mpc. Observations of the substructure, distribution, luminosity,
and evolution of galaxy clusters are therefore likely to provide
signatures of the underlying cosmology of our Universe, and can
be used as cosmological probes in the easily observable redshift
range
.
Thomas et al. [54] have investigated the internal structure of galaxy clusters
formed in high resolution N-body simulations of four different
cosmological models, including standard, open, and flat but low
density universes. They find that the structure of relaxed
clusters is similar in the critical and low density universes,
although the critical density models contain relatively more
disordered clusters due to the freeze-out of fluctuations in open
universes at late times. The profiles of relaxed clusters are
very similar in the different simulations, since most clusters
are in a quasi-equilibrium state inside the virial radius and
follow the universal density profile of Navarro et al. [45]. There does not appear to be a strong cosmological dependence
in the profiles, as suggested by previous studies of clusters
formed from pure power law initial density fluctuations [25]. However, because more young and dynamically evolving clusters
are found in critical density universes, Thomas et al. suggest
that it may be possible to discriminate among the density
parameters by looking for multiple cores in the substructure of
the dynamic cluster population. They note that a statistical
population of 20 clusters can distinguish between open and
critically closed universes.
The evolution of the number density of rich clusters of galaxies
can be used to compute
and
(the power spectrum normalization on scales of
Mpc) when numerical simulation results are combined with the
constraint
, derived from observed present-day abundances of rich clusters.
Bahcall et al. [9] computed the evolution of the cluster mass function in five
different cosmological model simulations and found that the
number of high mass (Coma-like) clusters in flat, low
models (i.e., the standard CDM model with
) decreases dramatically by a factor of approximately
from
z
=0 to
. For low
, high
models, the data results in a much slower decrease in the number
density of clusters over the same redshift interval. Comparing
these results to observations of rich clusters in the real
Universe, which indicate only a slight evolution of cluster
abundances to redshifts
, they conclude that critically closed standard CDM and Mixed
Dark Matter (MDM) models are not consistent with the observed
data. The models which best fit the data are the open models with
low bias (
and
), and flat low density models with a cosmological constant (
and
).
The evolution of the X-ray luminosity function, and the size and
temperature distribution of rich clusters of galaxies are all
potentially important discriminants of cosmological models. Bryan
et al. [16] investigated these properties in a high resolution numerical
simulation of a standard CDM model normalized to COBE. Although
the results are highly sensitive to grid resolution (see [6] for a discussion of the effects from resolution constraints on
the properties of rich clusters), their primary conclusion, that
the standard CDM model predicts too many bright X-ray emitting
clusters and too much integrated X-ray intensity, is robust,
since an increase in resolution will only exaggerate these
problems.