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 of 
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 observable redshift range 
.
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. [22]
computed the evolution of the cluster mass function
in five different cosmological model simulations and find 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 result 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
0.5-1, 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 
).
Several groups [44, 50
] have examined the properties of
X-ray clusters in high resolution numerical simulations of a standard
CDM model normalized to COBE. Although the results are very sensitive
to grid resolution (see [15
] 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. On the other hand, similar calculations
with different cosmological models [50, 46] suggest reasonable
agreement of observed data with Cold Dark Matter + cosmological
constant ( 
CDM), Cold + Hot Dark Matter (CHDM), and Open or
low density CDM (OCDM) evolutions due to different universal
expansions and density power spectra.
- K, and is described by the Compton y
parameter
where 
cm 
is the Thomson
cross-section, 
, 
and 
are the
electron rest mass, density and temperature, c is the speed of
light, 
is Boltzmann's constant, and the integration is
performed over the photon path.
Photon temperature anisotropies are related to the y parameter by
in the Rayleigh-Jeans limit.
The kinetic SZ effect is a less influential Doppler shift resulting
from the bulk motion of ionized gas relative to the rest frame
of the CMB.
Springel et al. [117] used a Tree/SPH code to study
the SZ effects in a CDM cosmology with a cosmological constant. They
find a mean amplitude for thermal SZ ( 
)
just below current observed upper limits, and
a kinetic SZ about 30 times smaller in power.
Da Silva et al. [60] compared thermal SZ maps in three
different cosmologies (low density + , critical density,
and low density open model). Their results
are also below current limits: 
for low density models with contributions from over a broad
redshift range 
,
and 
for the critical density model with
contributions mostly from z<1.
However, further simulations are needed to explore the
dependence of the SZ effect on microphysics, i.e., cooling,
star formation, supernovae feedback.
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Computational Cosmology: from the Early Universe to the Large Scale Structure Peter Anninos http://www.livingreviews.org/lrr-2001-2 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |