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8. Applications to cosmology

8.1. Dwarf ellipticals as distance indicators

Although they are faint, by sheer dint of numbers dE galaxies offer an attractive source for estimating the distances, or at least the relative distances, to nearby clusters. The association of most of the dE galaxies with the relaxed cores of clusters seems unambiguous, thus minimizing the uncertainties in cluster membership that hamper distance estimates based on the Tully-Fisher relation for late-type galaxies. Furthermore, it appears possible to derive purely photometric distance indicators for dE galaxies, which may somewhat atone for the difficulty of observing them.

The surface-brightness-luminosity relation has been used by Caldwell and Bothun (1987) and Ferguson and Sandage (1988) to estimate the relative distances to the Virgo and Fornax clusters. The scatter in this relation is much larger than for the Dn - sigma or Tully-Fisher relations, the deviation from a linear fit to the µe vs. BT relation being 0.8 mag for the Ferguson and Sandage (1988) Fornax cluster sample. However, the mean of the relation can be determined to comparable accuracy due to the increased numbers of galaxies. Caldwell and Bothun (1987) derived a Fornax/Virgo distance ratio of 0.8 from the µ0 - BT relation, while Ferguson and Sandage (1988) arrived at a ratio of 1.0, from consideration of the µe - BT relation, and suggested that the previous result may have been biased due to the selection of galaxies in the Virgo cluster photometric sample.

Bothun et al. (1989) estimated relative distances to the Virgo, Fornax, and Centaurus clusters using a subset of dE galaxies with well-defined exponential profiles, and assuming that the scale-length for such galaxies is constant. Later work by Bothun et al. (1991) suggests that the distribution of scale-lengths for dE galaxies in general is a steeply rising power-law (N(alpha) propto alpha-2). While this does not explicitly disprove the claim that dE's with pure exponential profiles all have the same scale length, it raises the possibility that distance estimates based on constant alpha could be subject to strong selection biases, for example based on the criteria used to decide whether galaxies are well fit by exponentials.

The increasing curvature of dE surface-brightness profiles with luminosity (Binggeli and Cameron 1991) provides another possible distance indicator. Young and Currie (1994) parametrize dE profiles with a generalized de Vaucouleurs law I (r) = I0 exp [-(r / alpha)n], and find a reasonable correlation of n with total magnitude for the Caldwell and Bothun (1987) Fornax cluster sample. Based on comparison with four local dE's, they estimate a distance of 13.8 Mpc for the Fornax cluster. The major difficulty in using such a relation to estimate distances is probably the ability to determine n, and the fact that n and total magnitude are highly correlated. The authors estimate that they can determine n to better than ± 0.06, but this estimate is based on the typical shot noise in the 1-d profiles and the uncertainty in the sky determination, rather than on a proper reminimization chi2 over all the other relevant photometric parameters (galaxy center, orientation, ellipticity, central surface brightness, and scale length) for different assumed values of n.

All of the above distance indicators are sensitive to selection biases, both in the standard Malmquist sense, and in the sense that most of the existing samples of dE galaxy CCD photometry are biased by surface-brightness in one way or another (see Sect. 4.3). Reasonably complete and unbiased samples could be constructed brighter than MB approx -13 for the Virgo and Fornax clusters, but more distant clusters will be progressively affected by interlopers, such that dE distance indicators may lose their usefulness beyond v approx 5000 km s-1.

To obtain absolute distances using dE's requires local calibrators. For an assumed distance of 22 Mpc, the extrapolation of Virgo cluster surface-brightness-magnitude relation does not line up perfectly with the Local Group dE's, suggesting a closer distance for Virgo. However, it is difficult to place the resolved Milky Way companions on the same scale due to uncertainties in their photometry. Young and Currie (1994) used NGC 205, NGC 185, NGC 147, and the Fornax dwarf for calibration, and also found a result favoring a short distance scale. While such distances cannot be taken too seriously for the reasons cited above, in principle there are actually more local calibrators for such photometric distance indicators than for other techniques, e.g. the Planetary Nebula luminosity function (Jacoby 1989), or surface-brightness fluctuations (Tonry and Schneider 1988). The difficulty is in getting precise photometry, and in providing a convincing physical argument for why the photometric correlations of dE galaxies in clusters should be the same as those in the Local Group.

Finally, dE galaxies may offer useful targets for distance estimates based on surface-brightness fluctuations. The amplitude of the fluctuations is actually greater for dE galaxies than for giant ellipticals, due to the lower surface density of stars and the lower metallicity (Bothun et al. 1991). However, the required exposure times are still much longer for dE's. Counteracting that is the availability of local calibrators, of the same luminosity and color as the more distant target galaxies for which fluctuations can be measured directly and computed from color-magnitude diagrams. This may circumvent, or at least provide a check on current absolute distances based on a calibration to M31, M32, and NGC 205 (Tonry 1991).

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