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

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5. THE LUMINOSITY FUNCTION FOR DIFFERENT HUBBLE TYPES

The first evidence that different Hubble types have different LFs was due to Holmberg (1958, 1969); he showed, in particular, that the LF of spirals does not follow a Zwicky (1942, 1957) exponential, but that it has a maximum instead. Subsequent studies of the LF that distinguished between types generally did not go to faint enough levels to see the effect. At the bright end the LFs of different types are surprisingly similar (cf. TYS), which seemingly supports the notion of a universal LF. As is shown below, the type-specific differences occur only at fainter luminosities.

Of the many LF studies already discussed in Section 4, several did in fact differentiate, if only partially, with respect to type. Following Holmberg, these are, for the field LF, Shapiro (1971), Christensen (1975), Turner & Gott (1976b), TYS, Davis & Huchra (1982), and Ellis (1983). The LFs of E and S0 galaxies in the field were determined by van den Bergh & McClure (1979) and by Choloniewsky (1985). Type-differentiated LFs in clusters were explored by the Oxford group (for references, see Section 4.1) and, in the case of the Fornax cluster, by Jones & Jones (1980) and Caldwell (1987).

However, these investigations were too limited in absolute magnitude and/or in type resolution to reveal any significant type-dependent differences. The necessary magnitude range is available only for the local field and for very nearby clusters, while the type resolution calls for large-scale plates instead of Schmidt plates. These requirements are best fulfilled in the case of field galaxies by the "10-Mpc sample" (Kraan-Korteweg & Tammann 1979; revised by Kraan-Korteweg & Binggeli 1987) and the RSA (cf. Tammann et al. 1980), and in the case of clusters by Virgo (SBT) and Coma (Thompson & Gregory 1980). The following discussion is mainly based on these latter investigations.

An overview of the LFs of different morphological types for the local field and for the Virgo cluster is shown in Figure 1. The LFs are shown as smoothed histograms of logvarphi(M) versus absolute blue magnitude MBT. The zero point of the logvarphi(M) scale is arbitrary, but the relative frequency of the types within the same sample (field or Virgo) is maintained.

The data for the Virgo cluster (Figure 1, bottom) are from SBT, where a somewhat different summary diagram of the smoothed LFs was chosen (their Figure 21). The completeness limit lies at mBT ~ 18, which with (m - M)0 = 31.7 corresponds to MBT ~ -13.7. Extrapolations of the LFs beyond this limit are drawn as dashed lines. The LFs for E, S0, spiral, Irr, and dE galaxies are shown as solid lines within the completeness range. The spirals are further subdivided into Sa + Sb, Sc, and Sd + Sm systems; the subtypes are shown as dotted lines. The Irr class comprises the normal and dwarf Im's and BCDs; the latter class is also separately shown as a dotted line (for illustrations of the dwarf classes, see Sandage & Binggeli 1984). Two classes of galaxies are not shown in Figure 1 so as to avoid overcrowding, namely the rare dS0s and the exponentially increasing dE/Im's. It is not clear yet whether the dE/Im's constitute a physical transition between dEs and Im's or a gray zone because of classification problems (Sandage & Binggeli 1984, SBT). The heavy line in Figure 1 represents the total over all galaxies (including the types not individually shown).

The field data (Figure 1, top) come from two sources. For types other than E+S0, the "10-Mpc sample" (Kraan-Korteweg & Tammann 1979) was used. While the LFs of this sample were previously derived (Tammann & Kraan 1978, Tammann 1986), we use here only the 121 member galaxies in groups from a revised version (Kraan-Korteweg & Binggeli 1987). The restriction to (well-studied) groups (Local Group, M81, M101, etc.) ensures a completeness limit of roughly MBT ~ -15. Because the sample contains only five E + S0 galaxies, their LFs are from the RSA sample as determined by TYS. The completeness limit lies here at MBT ~ -18. The RSA LFs have been scaled such that the Es and S0s - in accord with the RSA - each contribute 5% of the total brighter than MBT = -18.

Figure 1

Figure 1. The LF of field galaxies (top) and Virgo cluster members (bottom). The zero point of logvarphi(M) is arbitrary. The LFs for individual galaxy types are shown. Extrapolations are marked by dashed lines. In addition to the LF of all spirals, the LFs of the subtypes Sa + Sb, Sc, and Sd + Sm are also shown as dotted curves. The LF of Irr galaxies comprises the Im and BCD galaxies; in the case of the Virgo cluster, the BCDs are also shown separately. The classes dS0 and "dE or Im" are not illustrated. They are, however, included in the total LF over all types (heavy line).

The type binning in Figure 1 is the same for the field as for the Virgo cluster. An exception is the BCDs, whose known number in the field sample is insignificant. Extrapolations beyond the completeness limits are again shown as dashed lines. The dE population of the field is not well known, and this type is therefore shown as a broken line. The dEs are further discussed in Section 5.2.

Comparing the LFs for the field and the Virgo cluster in Figure 1, one should remember that the Virgo data are much more reliable than those of the field. While the Virgo sample encompasses ~ 1300 member galaxies, the number of field galaxies that determine the smoothed LFs is small and drops in some cases below 10. Moreover, the Virgo galaxies could be classified from a homogeneous set of large-scale plates, whereas the types of the field sample come from various sources. Finally, the magnitudes of some of the fainter field galaxies are quite uncertain. As a consequence the Virgo cluster is taken as a basic reference in what follows; the field LFs are used only to look for gross deviations from the Virgo LFs. It is an important problem for the future to determine the field LF more accurately.

In the following the LFs are discussed type by type and are then summarized in Section 5.4.

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