10.1 THE D_n- RELATION FOR ELLIPTICAL GALAXIES

The use of elliptical galaxies as distance indicators developed from studies aimed at determining their physical properties. The discovery of the relationship between luminosity and central velocity dispersion, L ⁴, by Faber and Jackson (1976) marks the beginning of the potential use of normal elliptical galaxies as standard candles. Following that discovery, automatic, quantitative techniques based on Fourier or cross correlation methods for measuring velocity dispersions came into frequent use (Sargent et al. 1977; Tonry and Davis 1980; Davies 1981). The use of these quantitative methods led to a growth of work on the properties and distances of elliptical galaxies, notably the suggestion by Terlevich et al. (1981) of a second parameter at work in the Faber-Jackson relation and the use of that relation by Tonry and Davis (1981) to measure the infall of the Local Group towards the Virgo cluster. The uncertainty in the distance to a single galaxy in Tonry and Davis' use of the Faber-Jackson relation was 32%.

Further work investigating the nature of the second parameter in the Faber-Jackson relation led to the development of the D_n- relation, where the diameter D_n incorporates both luminosity and surface brightness into a single parameter (Dressler et al. 1987b). The largest uniform body of D_n- data was collected in the first half of the 1980s by the collaboration which has become known as the ``7 Samurai'' (7S) and is to be found in Davies et al. (1987), and Burstein et al. (1987); the work is summarized in Faber et al. (1989). These data formed the basis for the first and currently most extensive application of the method. They combined velocity dispersions measured using quantitative analysis of digital spectra with diameters derived from concentric aperture photoelectric photometry and some CCD photometry. By incorporating surface brightness as the second parameter in the Faber-Jackson relation they formulated a new distance indicator, ^x / D_n, (Dressler et al. 1987b) where D_n is defined as the diameter which encloses a mean blue surface brightness of 20.75 magnitudes per square arcsec. [Lucey (1986) had noted previously that the use of fixed aperture magnitudes in the L, relation produced a smaller scatter than the use of total magnitudes.] D_n provides a convenient and close to optimum way of combining luminosity and surface brightness into a single parameter (see Sec. 10.3.1).

The mean surface brightness level for D_n was chosen to minimize the scatter in the new distance estimator and had the advantage that the aperture photometry measurements frequently spanned the diameter value, allowing D_n to be determined by interpolation using the r^1/4 law curve of growth. For the 7S sample the uncertainty in relative distance to a single galaxy was 23%. The 7S used these data to measure the pattern of peculiar motions of galaxies and clusters over the whole sky out to recession velocities of 8000 km s^-1 in the reference frame of the cosmic microwave background. They discovered a large scale coherence to this pattern (Dressler et al. 1987a), from which they inferred that galaxies in a large volume partake in a large scale flow towards l = 307°, b = 9° (Lynden-Bell et al. 1988, LFBDDTW). They postulated that this flow arises from the gravitational attraction of an over-dense region centered on 4500 km s^-1, extending to the Local Group which Alan Dressler named the ``The Great Attractor''. Subsequent studies using the method have centered on attempts to confirm (or negate) the existence of the Great Attractor. A review of the status of the Great Attractor is beyond the scope of this discussion; a description of a modified Great Attractor model can be found in Faber and Burstein (1989) and a comprehensive evaluation of the present situation can be found in Burstein et al. (1990, BFD).

The availability of sensitive, linear CCDs on small telescopes together with the development of sophisticated analysis software has led to the accurate photometric measurement of luminosity and effective radius (R_e) for a large number of elliptical galaxies (e.g., Lauer 1985; Djorgovski 1985). Both Lauer (1985) and Djorgovski and Davis (1987) discovered the same second parameter relation for elliptical galaxies independently of the 7S (see Faber et al. 1987) using data of this kind. Djorgovski and Davis (1987) introduced the idea of elliptical galaxies populating a ``fundamental plane'' in the log L - log R_e - log space, so that the Faber-Jackson relation is the projection of that fundamental plane onto the L - plane. Note that while both methods rely on the correlation of a global parameter (luminosity and surface brightness) with the velocity dispersion determined locally at the galaxy center, the method works in a statistical sense as there is a good correlation between the central value of velocity dispersion and that averaged over a more representative volume of the galaxy.

CCD imaging data provide (1) the potential for a more complete photometric characterization of the galaxy and therefore sensitivity to peculiarities in the morphology (e.g., Bender et al. 1989; Peletier et al. 1990), (2) a post observing opportunity to remove superimposed interfering star and galaxy images, and (3) a greater control over the way in which photometric parameters are determined. These advantages make CCDs the detectors of choice for future work despite the increase in reduction and analysis effort and the added overhead required for absolute calibration.

The distribution and physical properties of elliptical galaxies make them attractive as potential distance indicators because:

(1) They are luminous galaxies so that their global properties can be measured accurately at large distances. The D_n- method can be used to measure distances both within the Local Supercluster and out to distances more than twice that of the Coma cluster.

(2) They are strongly clustered so that many galaxies can contribute to the determination of the distance to an aggregate of galaxies. This increases the precision of the distance estimate and reduces systematic ``Malmquist-like'' biases.

(3) They have a single dominant old stellar population and are free of the obscuring effects of dust.

The method is, however, potentially sensitive to variations in the physical properties of ellipticals: residual star formation, the unknown distribution of intrinsic shapes, variations in the degree of rotational support, the presence of central velocity dispersion anomalies, and/or the presence of a weak disk.

Unfortunately there are no nearby examples of luminous elliptical galaxies that can be used for absolute calibration using primary indicators. Furthermore, there is no theoretical basis for an absolute calibration of the D_n- relation. Thus, the method is best suited to measuring relative distances that can then be calibrated by some of the other methods discussed elsewhere in this review. For this reason the method has been applied primarily to measure the peculiar motions of galaxies and aggregates of galaxies, rather than to derive absolute distances for individual galaxies.