Annu. Rev. Astron. Astrophys. 1988. 26: 509-560 Copyright © 1988 by Annual Reviews. All rights reserved

1.3. History of Determining the General Luminosity Function

Soon after the general acceptance of nebulae as galaxies, and following Knut Lundmark's studies of resolved stars in M33, E.J. Opik's dynamical determination of the distance to M31, and Edwin Hubble's discovery of Cepheids in M31, M33, and NGC 6822, Hubble began a study of the spread of M for galaxies. It soon became evident that the scatter of the velocity-apparent magnitude relation (the Hubble diagram) was small for the Shapley-Ames galaxies studied by Humason (1936), which included a few velocities then known from the beginning of N.U. Mayall's Lick Observatory program. On the assumption of a linear velocity-distance relation, this meant that the spread in M for these galaxies was also small. This led Hubble (1936a, b, c) to claim that a Gaussian distribution held for (M) with = 0.84 mag. This distribution was obtained from the residuals of the velocity-magnitude relation and was seemingly confirmed by an independent method based on the apparent magnitudes of the brightest resolved "stars," which later were found to be mostly H II regions.

Hubble's Gaussian form was later argued to be incorrect because of neglected selection effects (Zwicky 1942, 1957, 1964), with the true (complete) LF being an increasing exponential to very faint dwarfs. Holmberg (1950) showed that the addition of the known faint dwarfs in the Local Group indeed skewed Hubble's symmetrical Gaussian on the faint side. Abell's (1962, 1964, 1972) study of the LF of clusters was the first convincing evidence that dwarf galaxies have an exponentially rising LF, contrary to the bounded (M) on both the bright and faint end for spirals, S0, and high-surface-brightness elliptical galaxies. The publication by Reaves (1956) of data on dwarfs in the Virgo cluster, anticipated by Baade (1950) and discussed earlier by C.D. Shane (quoted in Baade 1950), began to convince Zwicky's critics that his 1942 conjecture for an exponential faint tail to (M) was correct. Krupp (1974) later published the most comprehensive cluster LF to date [following the important work of Rood (1969) in the Coma cluster] based on Palomar Observatory 5-m reflector plates. Modern work in the Coma cluster by Thompson & Gregory (1980) will soon be superseded by an even more comprehensive survey by the same authors, again in Coma.

Holmberg's (1969) study of companions to field giants suggested (only a few redshifts were available) that the general LF outside the great clusters also has an exponentially rising faint end rather than a bound as in Hubble's first formulation.

In recent years it has become clear that both Hubble and Zwicky were correct for the types of galaxies each discussed. Hubble's list was almost exclusively high-surface-brightness galaxies, whereas Zwicky's faint rising exponential tail almost entirely contained galaxies of low surface brightness, none of which were in Hubble, Humason, or Mayall's early redshift program. The shapes of the two luminosity functions, (nearly symmetric Gaussians for the high-SB cases, ever-increasing exponentials for low-SB cases) provide the first and most obvious example of a difference in the specific _T(M) functions for different types. Other, more modern examples are the first-ranked cluster E galaxies, which have an exceptionally small dispersion of 0.3 mag and a nearly Gaussian (M) (Sandage 1972, Sandage & Hardy 1973, Schneider et al. 1983), and ScI spirals, which have 0.7 mag and also a nearly Gaussian (M) (Sandage & Tammann 1975).

Studies of the general LF of the field were hampered early on by the sparseness of the redshift data for the samples studied. Early determinations of the bright end of the field function (van den Bergh 1961, Kiang 1961) depended on the redshift catalog of Humason et al. (1956; hereinafter HMS), with magnitudes from Pettit (1954) corrected for aperture effect by HMS. This redshift sample was not appreciably increased until the late 1970s. The most comprehensive studies before the large new redshift surveys began are those of Shapiro (1971) and Christensen (1975). These studies were innovative in that they divided the discussion into morphological types, which was the beginning of our present emphasis on the specific _T(M) function for each type.

An important review by Felten (1977) of the work on the general field LF summarizes nine independent studies of the shape of (M) for "field" galaxies and pays particular attention to the absolute normalization. This is treated as the density function in Section 2, and it normalizes (M) <D(r)> into units of the number of galaxies at M ± 1/2 dM per cubic megaparsec.

Felten's review was the last to summarize work before the new data from comprehensive redshift surveys began to be analyzed. The first of these new data sets was the completion of redshift coverage of Shapley-Ames galaxies on those galaxies not measured by Humason and Mayall (Sandage 1978). These data were combined with all others in the literature to produce the Revised Shapley-Ames Catalog (Sandage & Tammann 1981; hereinafter RSA), which was analyzed by TYS, accounting for selection effects. A mean total (general) LF was derived that was separated into various spiral types and van den Bergh luminosity classes. The result was compared with the LF for ellipticals. From this large sample, the average given in Equation 2 was derived, which is similar to the values of the luminosity density determined previously (reduced to the same value of H₀) from the many studies already referenced.

Redshift surveys to fainter magnitudes also began to be analyzed. A result by Kirshner et al. (1979) for their special regions, where redshift distributions to fixed magnitudes had been obtained, was compared with the so-called universal Schechter (1976) general function. Davis & Huchra (1982) later initiated the analysis of the field galaxy sample of the Center for Astrophysics (CfA) redshift survey, complete in various regions to m 14.2.

A new development was the study by Tammann & Kraan (1978), who analyzed a volume-limited sample rather than one that was flux-limited such as the RSA or the CfA survey (Huchra 1985). They obtained separate luminosity functions for various Hubble types (i.e. the specific _T(M) functions). The analysis was based on their distance-limited catalog for galaxies within a corrected redshift of 500 km s^-1 (Kraan-Korteweg & Tammann 1979).

Finally, still commenting on studies of the field LF, we note the new methods of analysis introduced by Turner (1979), Kirshner et al. (1979), Sandage et al. (1979), and Choloniewski (1985, 1986, 1987) to deal with selection effects.

Studies of the LF of clusters is inherently easier than for field galaxies because the problem of knowing individual distances is circumvented. The work of Abell and Krupp already has been mentioned above. Rood's (1969) work on the Coma cluster initiated the modern methods of cluster photometry. Early examples are the studies by Oemler (1974), Godwin & Peach (1977), Dressler (1978), and Kraan-Korteweg (1981) of the Virgo cluster, which are the first modern deep studies of this cluster.

Most of the studies mentioned in this section were concerned with the general LF integrated over all Hubble types and environmental densities. The remainder of this review sets out in a new direction, hinted at in some of the earlier referenced papers - namely, the work with the individual specific functions _T(M).