Annu. Rev. Astron. Astrophys. 1988. 26: 509-560
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6.2. Toward a Luminosity Function-Density Relation

It is easy in principle to calculate the local density in any environment and to construct and intercompare varphiT(M) for different density bins. The problem is that the binning must, by necessity, be very coarse because with finer binnings the galaxy numbers would be too small to give any weight to the resulting varphiT(M). The coarsest binning is the traditional "field"-"cluster" separation emphasized throughout this review. But the LFs for different types have usually not been compared for the two environments, or at most only at the bright end, where every LF is approximately the same (cf. Sections 4, 5). The treatment of a cluster as a mean environment is quite unsatisfactory because the local (projected) density in a cluster can vary by a factor of 100 (Dressler 1980); indeed, the morphology-density relation applies even to different regions within a given cluster (which also proves beyond doubt either that virial mixing has not occurred or that galaxies have changed morphological type within a cluster!).

Godwin & Peach (1977) were the first to look for differences of the LF within a cluster. Constructing varphi(M) for the Coma cluster separately for an inner and an outer zone, they found a significant deficiency of bright galaxies in the inner part (neglecting the two dominant cD galaxies). The same phenomenon for the inner and outer regions of two other clusters has recently been reported by Lugger (1987). Probably this is simply a refinement of the observation of Oemler (1974) and Dressler (1978) that cD clusters on the whole have a deficit of bright galaxies, perhaps to be interpreted as the result of merging and tidal stripping (Dressler 1984; see also Section 4.1).

Dressler (1980) has compared the LFs of S + Irr and S0 galaxies in low-density and high-density regions of his 55 clusters and found no evidence for any difference. B. Binggeli (unpublished work) did the same for the Virgo cluster alone (which is feasible because of the large number of known members), separately for E, S0, dE, spiral, and Irr galaxies, and again found no clear indication that the type-specific cluster LFs depend on the local density. There is only a hint for E and S0 galaxies to be brighter in higher density regions.

The topic of the LF-morphology-density relation for field galaxies has been addressed by de Souza et al. (1985), Choloniewski & Panek (1987), and Einasto & Einasto (1987). All three studies are essentially based on the CfA redshift survey (Huchra et al. 1983). In the first two studies the local spatial densities have been estimated by a nearest-neighbor algorithm. No density dependence of the LFs was found for the main Hubble types. (A marginal effect was reported for S0s.) Instead of constructing full LFs, Einasto & Einasto (1987) have chosen to calculate the mean absolute magnitude of the three brightest galaxies for different morphological types and environments. Evidence was found that the brightest galaxies in groups and clusters are brighter than those in the field by up to 1 mag; this effect is claimed not to be caused by the Malmquist bias.

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