![]() | Annu. Rev. Astron. Astrophys. 1988. 26:
509-560 Copyright © 1988 by Annual Reviews. All rights reserved |
As mentioned in Section 1.3, Zwicky (1942) postulated the exponential nature of the LF. Although he had derived the result as a theoretical necessity of thermodynamics rather than having found it observationally, he later claimed observational confirmation from cluster data (e.g. Zwicky 1957).
The completion of the Palomar Observatory Sky Survey in the late 1950s
initiated a host of cluster LF studies with Abell and his
collaborators as the driving force (for reviews, see
Abell 1962,
1972,
1975).
The basic hypothesis was that clusters of galaxies obey a
universal LF, which, in its integrated form
(M), can be
modeled by
two straight lines intersecting at a characteristic magnitude
M*
(sometimes referred to as the "knee"). Although Abell's shape of the
LF is no longer used, it is clearly a first approximation to the
Schechter (1976)
function in its asymptotic behavior at both the
bright and faint ends.
The modern, post-Abell cluster research began with Oemler (1974) who used large-scale plates with good morphological resolution and discussed a model-free LF. His work was followed up by many authors; a partial list in Table 3 sets out those rich clusters whose LFs have been determined since 1974. The quality and depth of these investigations vary widely. Some authors give only a crude LF for a distant cluster (e.g. Iannicola et al. 1987), while others achieve great morpological detail and/or drive for very faint (surface) magnitudes [e.g. Sandage et al. (1985) in the nearby Virgo cluster]. Most cluster studies have adopted the Schechter fitting law. An exception is the "Oxford group" (Austin & Peach 1974, Austin et al. 1975, Godwin & Peach 1977, Bucknell et al. 1979, Carter & Godwin 1979, Carter 1980, Godwin & Peach 1982), who have used model-free as well as Abell fits for their LFs.
Cluster | Investigators | Cluster | Investigators |
Virgo | Bucknell et al. 1979 | A1413 | Dressler 1978 |
Kraan-Korteweg 1981 | A1553 | Bucknell et al. 1979 | |
Sandage et al. 1985 | Yamagata et al. 1984 | ||
Fornax | Jones & Jones 1980 | A1656 | Oemler 1974 |
Caldwell 1987 | (Coma) | Godwin & Peach 1977 | |
A85 | Murphey 1984 | Thomson & Gregory 1980 | |
A98 | Dressler 1978 | Beckkman 1982 | |
A154 | Dressler 1978 | Lugger 1986 | |
A168 | Dressler 1978 | A1904 | Oemler 1974 |
Oegerle et al. 1986 | A1930 | Austin et al. 1975 | |
A194 | Oemler 1974 | A1940 | Dressler 1978 |
A274 | Dressler 1978 | A2029 | Dressler 1978 |
A400 | Oemler 1974 | A2065 | Bucknell et al. 1979 |
A401 | Dressler 1978 | (Corona | Borealis) |
A426 | Bucknell et al. 1979 | A2147 | Bucknell et al. 1979 |
(Perseus) | Egikyan et al. 1985 | Lugger 1986 | |
A539 | Oemler 1974 | A2151 | Oemler 1974 |
A569 | Lugger 1986 | (Hercules) | Bucknell et al. 1979 |
A665 | Oemler 1974 | Lugger 1986 | |
Dressler 1978 | A2175 | Oegerle et al. 1987 | |
A744 | Kurtz et al. 1985 | A2197 | Oemler 1974 |
A777 | Iannicola et al. 1987 | Lugger 1986 | |
A779 | Lugger 1986 | A2199 | Oemler 1974 |
A910 | Iannicola et al. 1987 | Bucknell et al. 1979 | |
A999 | Chapman et al. 1987 | Lugger 1986 | |
A1016 | Chapman et al. 1987 | A2218 | Dressler 1978 |
A1146 | Carter & Godwin 1979 | A2256 | Dressler 1978 |
A1228 | Oemler 1974 | Oegerle et al. 1987 | |
A1314 | Oemler 1974 | A2384 | Oegerle et al. 1987 |
A1367 | Oemler 1974 | A2634 | Lugger 1986 |
Godwin & Peach 1982 | A2670 | Oemler 1974 | |
Lugger 1986 | Dressler 1978 | ||
A1377 | Bucknell et al. 1979 | Bucknell et al. 1979 | |
(Ursa Major I) | 0004.8-3450 | Carter 1980 | |
A1413 | Austin & Peach 1974 | CA 0340-538 | Quintana & Havlen 1979 |
Oemler 1974 | Zw 1545.1+2104 | Oemler 1974 | |
A discussion of the individual cluster LFs is not given nor is a detailed intercomparison of the results. This has already been provided by Dressler (1984) in his review on the evolution of cluster galaxies. Instead, we concentrate on the investigations that covered several clusters in a search for systematic trends.
First indications for the nonuniformity of the cluster LFs are due
to Oemler (1974),
who classified clusters recording to galaxy content
as being "spiral-rich," "spiral-poor," and "cD." The mean LFs for these
three classes, which correlate with the kinematic properties of the
clusters, appeared to be marginally, but significantly, different.
However,
Schechter (1976)
fitted his expression to Oemler's clusters
and, following Abell, found a rather high degree of uniformity with
respect to the parameters
and M*. This came as a surprise because
significant differences could be expected in view of the cluster types
presumably being in different evolutionary stages. If so the result
had to be interpreted in the sense that cluster evolution had little
effect on the LF. From the near-agreement of the parameters
~ -1.25 and
MBT* ~ -21.0 for field
and cluster galaxies, Schechter further
concluded that the shape of the "general" LF is universal. Yet the
processes of tidal stripping and dynamical friction are bound to have
some bearing on the LF (cf.
Dressler 1984).
Dressler (1978)
consequently searched for deviations from the first-order universality
in 12 rich clusters and did indeed find significant
differences. Several clusters showed an unusually flat faint end
(
~ -1). Furthermore,
the data for cD clusters supported
Oemler's (1974)
observations of a steeper bright end than for non-cD clusters, which
was also suggested by
Bucknell et al. (1979)
and many others (as reviewed by
Dressler 1984).
The latter result could be interpreted as
an evolutionary effect where the central cD galaxy formed at the
expense of the next brightest cluster galaxies
(Miller 1983,
Malumuth & Richstone
1984,
Dressler 1984).
The question of whether the
first-ranked cluster galaxy is within the statistics of the cluster LF
or whether it is a singular object has been long debated and may now
have been settled in favor of the latter possibility (cf.
Dressler 1984,
and references therein) for cD clusters. The jury is still out,
however, for non-cD clusters [see
Sandage (1988)
in this volume for a review of the continuing debate].
Besides the cD effect, it has remained unclear which evolutionary
processes are actually responsible for the significant variance of
and M* among
Dressler's (1978)
clusters, although theoretical explanations have been suggested
(Dressler 1984,
Kashlinsky 1987).
Lugger (1986)
could not correlate the LFs of nine Abell
clusters with the cluster morphology.
Merritt (1984,
1985)
argued on
theoretical grounds that the cluster LF was determined very early
during the violent relaxation phase, and that correspondingly no
dependence of the LF on the present-day evolutionary stage of the
clusters should be expected.
An intriguing explanation of the variance of
and
M* among clusters has been offered by
Thompson & Gregory
(1980).
Using large-scale
plates of the Coma cluster, they established the LFs of E, S0, and
S+Im galaxies separately, from which they suggested that the LFs,
which are clearly different for different types, remained the same in
every cluster, but that the total LF as the sum over different types
varies according to the types mixture. By synthesizing clusters of
different type composition they were able to reproduce the variance of
and
M* observed by
Dressler (1978).
This hypothesis requires
additional tests from many clusters with detailed morphological
information that is presently only available for Virgo
(Sandage et al. 1985)
and Fornax
(Sandage & Ferguson
1988).
It should be noted
that modern, sophisticated LF studies like those of
Lugger (1986),
Oegerle et al. (1986,
1987),
and others are unsuitable for this
purpose because they are based on small-scale plates where
morphological binning gives unsatisfactory results. Thompson &
Gregory's hypothesis is discussed and supported further in
Section 6.
The limited data on the variance of the cluster LF can be explained satisfactorily as the effect of the first-ranked galaxies and the different type mixture. However, if the influence of the type mixture is denied, the remaining differences of the LF probably must be explained by evolution. Since this is not our preferred solution now, the reader is referred to the earlier review by Dressler (1984) for the consequences of this possibility.
The Schechter parameters are not listed in
Table 2 because the
results from individual investigations are too
inhomogeneous. Different magnitude systems are used, as well as
different fitting procedures. In some cases
and
M* were solved for,
whereas in others one of the Schechter parameters was fixed a
priori. A set of parameters that could be compared was provided by
Lugger (1986)
for nine clusters. Fitting simultaneously for
,
M*, and the normalization, she found for
a mean value of
= -1.24 ± 0.22 with
the brightest galaxy excluded, or
= -1.47 ± 0.19 if
it was included. As noted earlier by
Schechter (1976),
one obtains better
fits if first-ranked galaxies (or cD clusters) are
excluded. Therefore, Lugger's first-mentioned result is to be
preferred. It is in good agreement with Schechter's canonical average
of
= -1.25, which
still describes the faint-end slope of cluster
LFs fairly well. Yet, as mentioned before, there is no single value of
that applies to all
clusters
(Dressler 1978).
Moreover, field galaxies deviate significantly from this average, having an
closer
to -1.0 (cf. Section 4.2).
It should be stressed that what most cluster studies refer to as the
"faint end" lies still at fairly high luminosities, i.e.
MBT ~ -20
or -18 at best. The exponential for the faint end defined in this
way is usually a mere extrapolation of the Schechter function fitted
to bright galaxies. It was therefore quite surprising that the
Virgo cluster LF, which was measured to a much
fainter completeness limit of
MBT ~ -14, has confirmed a faint-end slope of
~ -1.25 (SBT). A
somewhat shallower slope of
~ -1.14 has been found
in a preliminary study of the Fornax cluster
(Caldwell 1987).
This study, however, used
small-plate scale material and may suffer incompleteness.
The range of M* for different clusters is given by Lugger (1986; see also Dressler 1978) as MBT* ~ -21.0 ± 0.7 (standard deviation) if cDs are excluded, or MBT* ~ -21.8 ± 0.6 if cDs are included. The former value is also recovered in the field (Section 4.2). The quoted magnitudes are reduced to H0 = 50 throughout this paper.
In addition to the variations in
and
M*, there are
clusters that seem to deny any choice of Schechter parameters
(Dressler 1978).
Although the significance of this effect is marginal because of the
limited size of cluster samples, it is not surprising. As mentioned
before, different Hubble types have quite different LFs. Depending on
the type mixture, they enter into the total LF with different
weight. It would be sheer coincidence if the latter could always be
represented by a simple analytical formula. The expected
mini-structure of the LF over all types is discussed further in
section 5 (cf.
Figure 1).