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2. Optical Properties of Galaxy Clusters

2.1. Typical Properties of Clusters and Groups

Clusters of galaxies are bound, virialized, high overdensity systems of galaxies, held together by the clusters self gravity. Rich clusters contain, by traditional definition (Abell 1958), at least 30 galaxies brighter than m3 + 2m (where m3 is the magnitude of the third brightest cluster member) within a radius of R appeq 1.5h-1 Mpc of the cluster center. This galaxy count is generally defined as the richness of the cluster. The galaxies in rich clusters move with random peculiar velocities of typically ~ 750 km s-1 (median line-of-sight velocity dispersion). This motion corresponds to a typical rich cluster mass (within 1.5h-1 Mpc) of ~ 5 × 1014h-1 Modot. In addition to galaxies, all rich clusters contain an intracluster medium of hot plasma, extending as far as the main galaxy concentration (R ~ 1.5h-1 Mpc). The typical temperature of the hot intracluster gas is ~ 5 kev, with a range from ~ 2 to 14 kev; the central gas density is ~ 10-3 electrons cm-3. The hot plasma is detected through the luminous X-ray emission it produces by thermal bremsstrahlung radiation, with Lx ~ 1044 erg s-1.

Like mountain peaks on earth, the high density rich clusters are relatively "rare" objects; they exhibit a spatial number density of ~ 10-5 clusters Mpc-3, as compared with ~ 10-2 galaxies Mpc-3 for the density of bright galaxies.

The main properties of clusters and groups of galaxies are summarized in Table 1 (Bahcall 1996). The table lists the typical range and/or median value of each observed property. Groups and poor clusters, whose properties are also listed, provide a natural and continuous extension to lower richness, mass, size, and luminosity from the rich and rare clusters.

Table 1. Typical Properties of Clusters and Groups.

Property a Rich clusters Groups and poor clusters

Richness b 30-300 galaxies 3-30 galaxies
Radius c (1-2) h-1 Mpc (0.1-1) h-1 Mpc
Radial velocity dispersion d 400-1400 km s-1 100-500 km s-1
Radial velocity dispersiond (median) ~ 750 km s-1 ~ 250 km s-1
Mass (r leq 1.5h-1 Mpc) e (1014-2 × 1015)h-1 curlyModot (1012.5-1014)h-1 curlyModot
Luminosity (B) f (6 × 1011-6 × 1012)h-2 Lodot (1010.5-1012)h-2 Lodot
(r leq 1.5 h-1 Mpc)
<curlyM / LB> g ~ 300h curlyModot / Lodot ~ 200h curlyModot / Lodot
X-ray temperature h 2-14 keV ltapprox 2 keV
X-ray luminosity h (1042.5-1045)h-2 erg s-1 ltapprox 1043h-2 erg s-1
Cluster number density i (10-5-10-6)h3 Mpc-3 (10-3-10-5)h3 Mpc-3
Cluster correlation scale j (22 ± 4)h-1 Mpc (R geq 1) (13 ± 2)h-1 Mpc
Fraction of galaxies in clusters or groups k ~ 5% ~ 55%

a In most entries, the typical range in the listed property or the median value is given. Groups and poor clusters are a natural and continuous extension to lower richness, mass, size, and luminosity from the rich and rare clusters.
b Cluster richness: the number of cluster galaxies brighter than m3 + 2m (where m3 is the magnitude of the third brightest cluster galaxy), and located within a 1.5h-1 Mpc radius of the cluster center (Section 2.2).
c The radius of the main concentration of galaxies (where, typically, the galaxy surface density drops to ~ 1% of the central core density). Many clusters and groups are embedded in larger scale structures (to tens of Mpc).
d Typical observed range and median value for the radial (line-of-sight) velocity dispersion in groups and clusters (Section 2.9).
e Dynamical mass range of clusters within 1.5h-1 Mpc radius (Section 2.10).
f Luminosity range (blue) of clusters within 1.5h-1 Mpc radius (Section 2.10).
g Typical mass-to-light ratio of clusters and groups (median value) (Section 2.10).
h Typical observed ranges of the X-ray temperature and 2-10-keV X-ray luminosity of the hot intracluster gas (Section 3).
i The number density of clusters decreases sharply with cluster richness (Section 7).
j The cluster correlation scale for rich (R geq 1, NR geq 50, nc = 0.6 × 10-5 h3 Mpc-3) and poor (NR gtapprox 20, nc = 2.4 × 10-5 h3 Mpc-3) clusters (Section 2.3, Section 7).
k The fraction of bright galaxies (gtapprox L*) in clusters and groups within 1.5 h-1 Mpc.

In the following subsections I discuss in more detail some of these intrinsic cluster properties.

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