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

5.3. Spiral and Irregular Galaxies

Long ago, Holmberg (1958, 1969) observed that the LF of spiral galaxies has a maximum. There are no dwarf spirals. The LF of all Virgo spirals can be modeled by a Gaussian with a mean of M_BT = -18.4 and a dispersion of _M = 1.5 mag (SBT). The overall form of the spiral LF is not too dissimilar to that of Es and S0s, especially at the brighter end (cf. Figure 1), which of course is the root of the simplified classical view that the LF does not depend on type. The spiral subtypes have been combined in Figure 1 into the classes Sa + Sb, Sc, and Sd + Sm so as not to complicate the diagram by a finer subdivision and to avoid small number statistics. The general trend is that early-type spirals are brighter in the mean than late-type spirals. But the Hubble spiral sequence does not order the galaxies monotonically into a luminosity sequence, because the mean luminosity of Sb (and Sab) galaxies is brighter than that of Sa's (SBT) (not shown in Figure 1 because of the binning). Sb galaxies are indeed among the intrinsically brightest galaxies in the Universe (cf. RSA, p. 94).

The spiral LFs in Figure 1 show a similar behavior for the field (top) and the Virgo cluster (bottom). They have the same maxima M_BT values in the cluster and the field, and further the subtypes are ordered in the same sequence. The difference shown in Figure 1 lies in the dispersion, but whether this difference is truly significant is questionable. To within the accuracy (small number statistics and inhomogeneous type determinations in the 10-Mpc sample) they are the same, and we advocate below that they are, in fact, the same.

The LFs of spirals become narrower near-Gaussians than those shown in Figure 1 when they are binned into the van den Bergh luminosity classes. Corresponding LFs for field galaxies in the RSA have been calculated by TYS, Kennicutt (1982), and Kraan-Korteweg et al. (1984).

If Im's are considered as the homologues of spirals, but with too low a mass to form spiral arms, the two classes of starforming galaxies may be fitted by a single LF. The result is a clearly peaked bell-shaped curve of which only the faintest end is ill defined (cf., for the field, Tammann & Kraan 1978; for Virgo, by construction from data given by BST). If Im's are taken as an individual class, their LF has a maximum at rather faint magnitudes, namely at M_BT ~ -16 for the Virgo cluster and roughly at -15 for the nearby groups, where this class dominates the faint end of the total LF (see Figure 1, but recall that the curve labeled "Irr" comprises Im's and BCDs; in the field the BCD contribution is negligible). The magnitude difference between the maxima in the Virgo cluster and the nearby groups is not significant, but the existence of the maxima seems to be well established by the data, particularly in the case of Virgo. It is therefore surprising that Scalo & Tyson (1987) have advocated recently that the Virgo maximum is an artifact because SBT have missed enough low-surface-brightness Im's owing to the iceberg effect to make the real LF an exponential. We return to this possibility below.

The LF of the Virgo BCDs is shown in Figure 1 (bottom). Because these galaxies are relatively easy to detect, their LF maximum at M_BT ~ -15.5 is certainly real, although there remains an ambiguity as to cluster membership for some high-surface-brightness BCDs that are difficult to distinguish from background objects on purely morphological grounds. BCDs are rare in the field and in groups (Tammann 1986), and this rarity is at most only partially due to the inhomogeneous classification of our corresponding sample. In any case, no LF can be given for them.

Im's, especially the faint and low-surface-brightness ones (which are rather smooth in appearance), are often hard to distinguish from dEs. In the Virgo cluster there is a whole class of objects for which the distinction is impossible. These objects were consequently called "dE or Im." The LF of these interlopers is exponential, similar to that of dEs (not shown in Figure 1; cf. SBT). It is unclear whether these systems run counter to a clear classification because of insufficient resolution, or whether they constitute a genuine (physical) transition between dE and Im. In favor of the latter hypothesis is the observation that the structural parameters of Im's and dEs are very similar - for instance, both exhibit exponential radial luminosity profiles (Wirth & Gallagher 1984, Binggeli et al. 1984, Kormendy 1985, Binggeli 1986, Bothun et al. 1986). This behavior has prompted several suggestions as to the origin of dEs and of diffuse dwarfs in general (dE+Im) (Lin & Faber 1983, Kormendy 1985, Dekel & Silk 1986, Silk et al. 1987). If, on the other hand, a large fraction of the transition class were true Im's, they could account for the exponential LF of Im's as suggested by Scalo & Tyson (1987).

5.4. Summary

Figure 1 clearly shows that the LFs of different types are widely different, and that the total LF over all types is the sum of many single, mostly bell-shaped curves. Discussing these samples in terms of a Schechter function over all types is like covering a wealth of details with a thick blanket. There are humps and bumps in the total LF according to the underlying type-specific LFs. The double wave of the Virgo total LF (Figure 1, bottom), for instance, cannot be modeled by a Schechter function. Figure 1 also reveals clearly the difference between the faint-end slopes of the total LFs of the field and of the Virgo cluster. No evidence is found that the type-specific LFs are different in the field and in Virgo. But owing to the variation of the type mixture as a function of environment, there cannot be a universal total LF. This conclusion leads to a new approach to the problem of universality, as set out in the following section.