Mass and Light distributions in Clusters of Galaxies - Henry A ...

1.1 Clusters of Galaxies
The space density of clusters in the local universe has been used to measure
the amplitude of density perturbations on ∼ 10 Mpc scales. Studying the
mass distribution within clusters is another probe of the non-linear growth
of structures. Numerical N-body and hydrodynamical simulations make clear
predictions for the structure of clusters, for example that they should have
a universal density profile (Dubinski & Carlberg 1991; Navarro et al. 1996)
and that their observable properties should satisfy some predicted scaling relations.
Comparing these predictions with observations is an important test
of CDM models.
Clusters form through the collapse of cosmic matter over a region of several
megaparsecs. Cosmic baryons, which represent approximately 10–15%
of the mass content of the Universe, follow the dynamically dominant dark
matter during the collapse. They fall into the gravitational potential of the
cluster dark matter halo so formed, while the collapse and the subsequent
adiabatic compression and shocks heat the intra-cluster medium (ICM). Hot
gas permeating the cluster potential well is then assembled, reaching temperatures
of several 10 7 K, and as it becomes fully ionized emits via thermal
bremsstrahlung in the X-ray band. Typically, clusters of galaxies have total
masses which exceed 1 × 10 14 M ⊙ , with some ∼ 85% in DM, ∼ 12% in IC
gas, and the rest in galaxies.
The main methods used to determine the cluster mass are through the
cluster galaxy velocities, through the effect of gravitational lensing, through
X-ray observations of the hot diffuse gas component, and through the Sunyaev-
Zel’dovich (SZ) effect. In this section, I review our understanding of the basic
properties of clusters formation, their mass, distributions and luminosity
functions. I review the methods of X-ray and SZ observations of clusters.
The field of gravitational lensing, which is the effect I rely on in my work, is
reviewed more thoroughly in the next section.
1.1.1 Cluster Mass from the Virial Theorem
Zwicky (1933) was the first to apply the virial theorem to estimate cluster
masses. A cluster mass is estimated by assuming all cluster galaxies are
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