and Cosmology

6.2 Galaxies in Clusters and Groups
omitted the Galactic disk region because the observation
of galaxies is considerably more problematic there,
due to extinction and the high stellar density (see also
Fig. 6.2).
Abell’s Criteria and his Catalog. The criteria Abell
applied for the identification of clusters refer to an
overdensity of galaxies within a specified solid angle.
According to these criteria, a cluster contains ≥ 50 galaxies
in a magnitude interval m 3 ≤ m ≤ m 3 + 2, where
m 3 is the apparent magnitude of the third brightest
galaxy in the cluster. 2 These galaxies must be located
within a circle of angular radius
θ A = 1.′ 7
(6.6)
z
where z is the estimated redshift. The latter is determined
by the assumption that the luminosity of the tenth
brightest galaxy in a cluster is the same for all clusters.
A calibration of this distance estimate is performed on
clusters of known redshift. θ A is called the Abell radius
of a cluster, and corresponds to a physical radius
of R A ≈ 1.5h −1 Mpc.
The so-determined redshift should be within the
range 0.02 ≤ z ≤ 0.2 for the selection of Abell clusters.
The lower limit is chosen such that a cluster can
be found on a single POSS photoplate (∼ 6 ◦ × 6 ◦ )and
does not extend over several plates, which would make
the search more difficult, e.g., because the photographic
sensitivity may differ for individual plates. The upper
redshift bound is chosen due to the sensitivity limit of
the photoplates.
The Abell catalog contains 1682 clusters which all
fulfill the above criteria. In addition, it lists 1030 clusters
that have been found in the search, but which do not
Sky Survey (DSS) that covers the full sky. Sections from the DSS can
be obtained directly via the Internet, with the full DSS having a data
volume of some 600 GB. Currently, the second Palomar Sky Survey
(POSS-II) is in progress, which will be about one magnitude deeper
compared to the first one and will contain data from three (instead
of two) color filters. This will probably be the last photographic atlas
of the sky because, with the development of large CCD cameras, we
will soon be able to perform such surveys digitally. The most prominent
example of this is the Sloan Digital Sky Survey, which we will
discuss in a different context in Sect. 8.1.2.
2 The reason for choosing the third brightest galaxy is that the luminosity
of the brightest galaxy may vary considerably among clusters.
Even more important is the fact that there is a finite probability for
the brightest galaxy in a sky region under consideration to not belong
to the cluster, but to be located at some smaller distance from us.
fulfill all of the criteria (most of these contain between
30 and 49 galaxies). An extension of the catalog to the
Southern sky was published by Abell, Corwin & Olowin
in 1989. This ACO catalog contains 4076 clusters, including
the members of the original catalog. Another
important catalog of galaxy clusters is the Zwicky catalog
(1961–68), which contains more clusters, but for
which the applied selection criteria are considered less
reliable.
Problems in the Optical Search for Clusters. The
selection of galaxy clusters from an overdensity of galaxies
on the sphere is not without problems, in particular
if these catalogs are to be used for statistical purposes.
An ideal catalog ought to fulfill two criteria: first it
should be complete, in the sense that all objects which
fulfill the selection criteria are contained in the catalog.
Second it should be reliable, i.e., it should not contain
any objects that do not belong in the catalog because
they do not fulfill the criteria (so-called false positives).
The Abell catalog is neither complete, nor is it reliable.
We will briefly discuss why completeness and reliability
cannot be expected in a catalog compiled in this
way.
A galaxy cluster is a three-dimensional object,
whereas galaxy counts on images are necessarily based
on the projection of galaxy positions onto the sky.
Therefore, projection effects are inevitable. Random
overdensities on the sphere caused by line-of-sight projection
may easily be classified as clusters. The reverse
effect is likewise possible: due to fluctuations in the
number density of foreground galaxies, a cluster at high
redshift may be classified as an insignificant fluctuation
– and thus remain undiscovered.
Of course, not all members of a cluster classified as
such are in fact galaxies in the cluster, as here projection
effects also play an important role. Furthermore,
the redshift estimate is relatively coarse. In the meantime,
spectroscopic analyses have been performed for
many of the Abell clusters, and it has been found that
Abell’s redshift estimates have an error of about 30% –
surprisingly accurate, considering the coarseness of his
assumptions.
The Abell catalog is based on visual inspection of
photographic plates. It is therefore partly subjective.
Today, the Abell criteria can be applied to digitized images
in an objective manner, using automated searches.
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