Annu. Rev. Astron. Astrophys. 1988. 26: 509-560
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7.1. Observational

7.1.1    NATURE OF RELEVANT SURVEYS    A condition of utmost importance in finding varphiT(M, D) in the field is that the galaxy sample to be studied have exquisitely defined selection criteria (i.e. complete to a given magnitude, to a given redshift, and to a given surface brightness for a given type). Since no sample is complete, the incompleteness must be known and factored into the solution for the effective volume surveyed.

7.1.2    MAGNITUDES    To date, field galaxy LF studies still rely on the Zwicky magnitude system, known to have systematic errors depending on the particular catalog volume (and therefore a function of declination) (Kron & Shane 1976). The errors are also functions of angular diameter and surface brightness [and therefore of type because SB = f (T) (Balkowski et al. 1974, Fisher & Tully 1975). The present methods for correcting this central and crucial data base remain patchwork and are unsatisfactory even at the +0.5 mag level, especially because the corrections are a function of magnitude.

What is needed is a new all-sky magnitude survey to at least the limit of the CfA redshift survey in the north and its companion redshift study in the south (da Costa et al. 1984). The European Southern Observatory (ESO) magnitude survey of A. Lauberts, now in progress, is a step in this direction.

All optical LFs of galaxies to date have been restricted to B (or mpg) magnitudes. Luminosity functions in other wave bands are of course possible. In fact, they would be nontrivial because of the color dependence on galaxy type and luminosity. Moreover, for high-redshift clusters the effects of the K-correction could be circumvented if their LFs were observed at the rest-frame wavelength of the B system.

7.1.3    SURFACE BRIGHTNESS    It was mentioned in Section 2 that the actual observational limit at the faint end is not defined by total magnitude, but rather by surface brightness. A systematic survey of low-surface-brightness objects would be extremely useful for getting a handle on the density of dwarfs in the local field and for further checking the possible existence of bright, low-surface-brightness galaxies (Disney 1976, Disney & Phillips 1983) that may threaten the varphi(M)'s. The new IIIaJ Palomar Schmidt survey appears promising in this respect (cf. Sargent 1986). A definitive solution to the problem of hidden objects of extremely low surface brightness (µ > 26B mag arcsec-2) is expected from D. Malin's technique (Impey et al. 1987).

The special study of low-SB galaxies is particularly important to solve the problem of the giant E/dwarf dE ratio as a function of density. Do dE dwarfs only occur as satellites of giant galaxies or in clusters, or do they occur isolated in the field? This question can be answered by testing if the alpha-parameter of the Schechter function fainter than, say, MBT ~-17 has the same value in the field (or even in very low-density regions of clusters) as in the cluster centers. The problem is central to the question of biased galaxy formation. It is equivalent to asking if the relative number of dwarfs to giants is larger in voids than in regions replete with giants. The survey of Binggeli et al. (1988), mentioned in Section 1.2.3, aims at answering this question.

A second problem concerning the varphi(M) for Im galaxies is also in need of solution. From both the 500 km s-1 (distance-limited) Kraan-Korteweg & Tammann (1979) sample and the Virgo cluster catalog (BST), the Im LF was found to show a maximum at MBT ~ -15.5, from which it decreases to zero. It would be an important result if all currently star-producing galaxies show such a maximum rather than an exponential increase toward fainter luminosities. However, Scalo & Tyson (1987) suggest that we have missed the faint SB Im's in our Virgo cluster survey (BST) and that the relevant varphi(M) does increase exponentially, similar to varphi(M) for dE galaxies. The problem hinges on the true nature of the transient class ("dE or Im") of BST, which has indeed an exponential LF. This obviously is a central point for ideas of galaxy formation and evolution and must be tested by observation rather than hypothesis.

7.1.4    MORPHOLOGICAL RESOLUTION    Once the LF is shown to depend on the morphological type, classifying galaxies becomes more important again. Most LF studies in clusters are based on Schmidt plates because they are convenient for covering the required large fields. However, such plates do not permit a fine type binning. Only the main classes, if any at all, can be distinguished for high-SB galaxies fainter than BT ~ 12 on such small-scale plates. Large-scale plates with a wide field of view are also needed for clusters, such as the Las Campanas Observatory plates used by Dressler (1980) for his study of 55 clusters. These plates would be ideal for obtaining varphi(M) for many clusters (the Las Campanas 100" telescope is in fact the only instrument suitable for the task) and for testing the hypothesis of universal varphiT(M)'s. Good, homogeneous classifications do exist for bright field galaxies (RC2, RSA) but not for the 500 km s-1 catalog (Kraan-Korteweg & Tammann 1979), which would otherwise be an ideal data base for the local varphi(M).

An enormous opportunity now exists to study many aspects of the field LF by combining magnitudes and morphological types with the modern redshift surveys (CfA survey, da Costa et al. 1984) that are designed to be complete to an intermediately faint Zwicky magnitude ( mpg ~ 14.2). Complete (all-sky) redshift surveys to fainter magnitudes are impractical, but smaller area surveys patterned after that of Kirshner et al. (1978) are in progress at several observatories. Accurate galaxy types for each of these large survey catalogs, especially for the low-SB late Hubble types, would enhance our knowledge by a quantum leap.

7.1.5    ENVIRONMENT    The correlation of varphi(M) with the environmental galaxy density requires reliable estimates of the latter. The densities should account for the total local galaxy number to a uniform lower luminosity limit. In the field, redshift data are needed for all candidate galaxies to exclude foreground and background objects. Methods to derive the local density are described by Postman & Geller (1984) and Choloniewski & Panek (1987). It is not yet clear how big a volume around each galaxy should be considered to achieve the best correlation between density and morphology, and hence varphi(M). In clusters one can derive smoothed three-dimensional radial density profiles if a cluster model is assumed. But subclustering, which may be important, can only be approximated at best because it will remain uncertain whether a given galaxy is connected to the local structure or whether it is projected onto it.

Good control of the environment is of course needed if the universality of the type-specific LFs, varphiT(M), is to be checked in a large number of field and cluster regions. Provided that varphiT(M) is fixed for any given type T, it will be possible to synthesize varphi(M) summed over all types as a function of the local density by weighting sets of standard varphiT(M)'s with the type fraction appropriate for that density. The shape of the synthetic total varphi(M) can then be compared with observations in corresponding regions without further regression to morphology.

The observed total varphi(M)'s may eventually turn out not to be a simple function of the local galaxy density, because this parameter alone can hardly determine the actual local type mixture. The latter must also depend on the dynamical history of a region. For instance, the present infall of galaxies, mainly of spirals, into the Virgo cluster will increase the spiral population of this cluster by ~ 40% over the next Hubble time (Tully & Shaya 1984) and will at the same time increase the local density. This is contrary to the average density-type relation that predicts a lower spiral fraction for higher density. On the other hand, the Hydra cluster, which lies isolated in space (Richter et al. 1982), can hardly increase its present spiral population.

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