ARlogo Annu. Rev. Astron. Astrophys. 1988. 26: 509-560
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5.2. Dwarf Elliptical Galaxies

E galaxies and dEs are morphologically distinct (Wirth & Gallagher 1984, Sandage & Binggeli 1984). Es are in general compact and of high surface brightness. Their compactness increases with decreasing luminosity (Kormendy 1980, 1985). In contrast, dEs are diffuse, i.e. they have low surface brightness. They become increasingly diffuse with decreasing luminosity (Baade 1944, Caldwell 1983, Binggeli et al. 1984, Bothun et al. 1986, Caldwell & Bothun 1987; for an illustration, see Sandage & Binggeli 1984). This dichotomy is classical: M32 versus NGC 205 and the Fornax and Sculptor dwarfs, as first discussed by Baade (1944). The distinction of Es and dEs, best visible in a plot of central surface brightness versus total magnitude (Kormendy 1985, his Figure 3) and suggested also by the different trends in an effective surface brightness-MBT diagram (BST, their Figure 8), must almost certainly mean that the two classes are of different origin (Kormendy 1985, Dekel & Silk 1986). This is also supported by the fact that the LFs of Virgo Es and dEs do not merge well into one LF. However, in the overlapping range (-18 ltapprox MBT ltapprox -16) Es and dEs, because of the cosmic scatter of their parameters, are sometimes hard to separate, even with the help of luminosity profiles (Caldwell & Bothun 1987). A confirmation that Es and dEs can presently be separated successfully might be seen in the fact that their LFs agree very well in the Virgo cluster (SBT) and Fornax cluster (Caldwell 1987), but the morphological separation of the latter cluster rests on plates with too small a scale to provide a stringent test.

The dwarf elliptical LF in the Virgo cluster can be modeled fairly well by a Schechter function with parameters alpha = -1.35 and M* = -17.4 (note the very steep increase at faint magnitudes compared with the field value of alpha approx -1). A notable deviation from a Schechter fit is the maximum at BT ~ 16 (MBT ~ -16; cf. Figure 1, bottom). This maximum was also found in the Fornax cluster by Caldwell (1987) but not confirmed by Ferguson & Sandage (1987). In the Virgo cluster, dEs are still rising exponentially at MBT ~ -14 (the completeness limit) and diffuse systems are known to exist down to MBT ~ -12. Still fainter systems are expected because local dEs are known at roughly MBT ~ -8 (Binggeli et al. 1984). The work of Impey et al. (1987) can be expected to shine light on this dark matter.

A detail worth noting is that dEs come in two subclasses: with or without central semistellar nucleus [cf. Sandage & Binggeli (1984) for illustrations]. The detectability of the nuclei is correlated with absolute magnitude; the mixing ratio of nucleated to nonnucleated dEs decreases from 1 to ~ 0.1 almost linearly from MBT ~ -18 down to ~ -12. Taken at face value, this means that the LF of nucleated dEs has a maximum, and that only the number of nonnucleated dEs takes off exponentially (SBT). However, the classification of nucleated dEs may be affected by another iceberg effect. Very faint nuclei may have passed unnoticed. The correlation of the galaxy and nucleus luminosities makes it possible, in fact, that all dEs have some kind of nucleus.

The field LF of dEs is difficult to establish because these galaxies are rare in low-density regions. As seen in the Virgo cluster (BST), their number frequency correlates strongly with local density. In this sense they behave like E galaxies, whose frequency-density relation was established by Dressler (1980). A systematic search for field dEs is being conducted by Binggeli et al. (1988). At present the only available evidence for fairly low-density regions comes from the Local Group and the M81 group. The latter was searched for dwarfs down to MBT ~ -12.5 (Börngen et al. 1982, Karachentseva et al. 1985; cf. also Sargent 1986), resulting in 10 dEs with -15 leq MBT leq -12.5. Their distribution is compatible with an exponential increase toward fainter objects. Therefore, the dashed curve of the field dEs in Figure 1 (top) is put in schematically with the shape of the LF of the Virgo dEs, but appropriately scaled to the relative frequency of dEs in the Local Group and the M81 group.

The dwarf S0s in the Virgo cluster have a narrow Gaussian LF centered on MBT ~ -17 (see SBT); they are not separately shown in Figure 1.

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