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Another ``classical'' distance indicator method that has been reborn in modern guise is photometry of brightest cluster galaxies (BCGs). As originally treated by Sandage and coworkers (Sandage 1972; Sandage & Hardy 1973), BCGs were considered to be good standard candles. As such, they were used to demonstrate the linearity of the Hubble diagram to relatively large distances and estimate H0. Any such estimate was and remains highly suspect, however, because of the difficulty of obtaining a good absolute calibration of the method. The scatter of BCGs as standard candles is around 0.30-0.35 mag, which compares favorably with methods such as TF or Dn-sigma.

A dubious assumption in the early work was that BCGs are true standard candles. Gunn & Oke (1975) first suggested that the luminosities of BCGs might correlate with their surface brightness profiles. Following this suggestion, Hoessel (1980) defined a metric radius rm = 10 h-1 kpc, and showed that the metric luminosity L(rm) ident Lm varied roughly linearly with a shape parameter alpha defined by

Equation 11 (11)

More recently, Lauer & Postman (1992) have shown that the correlation between Lm and alpha is better modeled by a quadratic relation. The Lauer & Postman (1992) data, along with their quadratic fit, are shown in the upper panel of Figure 7. Thus modeled, the typical distance error incurred by the BCG Lm-alpha relation is ~ 16%.

A slight hitch in applying the BCG Lm-alpha relation is the requirement of defining a metric radius rm for evaluating both Lm and alpha. This means that the assumed peculiar velocity of a BCG must be factored in to convert redshift to distance, and thus angular to linear diameter. In practice this is not a very serious issue. At the typically large distances (gtapprox 7000 km s-1) at which the relation is applied, peculiar velocity corrections have a small effect on Lm and alpha. Iterative techniques in which a peculiar velocity solution is obtained and then used to modify the rms, converge quickly (Lauer & Postman 1994).

Figure 7b
Figure 7. Top panel: the BCG Lm-alpha relation exhibited by the sample of Lauer & Postman (1992). Absolute magnitude within the metric radius rm is plotted against the logarithmic surface brightness slope at rm. The solid curve shows the quadratic fit to the data. Bottom panel: the Hubble diagram for the Lauer & Postman (1992) BCG sample. Apparent magnitude within rm is plotted against log redshift. The straight line plotted through the points has slope 5, the relation expected for a linear Hubble flow. The data used to make this figure were kindly provided by Marc Postman.

Modern scientific results based on BCGs are due to the pioneering work of Lauer and Postman (Lauer & Postman 1992; Lauer & Postman 1994, hereafter LP94; Postman & Lauer 1995). One important - and uncontroversial - such result has been confirmation, with unprecedented accuracy, of the linearity of the Hubble diagram to redshifts z appeq 0.05 over the entire sky. (The Hubble diagrams using SNe Ias (Section 6), by contrast, are not derived from isotropic samples.) This is shown in the lower panel of Figure 7. However, another result has been considerably more controversial, namely, the detection of a very large-scale bulk peculiar velocity by LP94. The linearity of the BCG Hubble diagram manifests itself with the smallest scatter when the velocities are referred to a local frame that differs significantly from that defined by the CMB dipole. Or, stated another way, the LP94 data indicate that the frame of Abell clusters out to 15,000 km s-1 redshift is moving with respect to the CMB frame at a velocity of ~ 700 km s-1 toward l appeq 350°, b appeq 50°. A reanalysis of the LP94 data by Colless (1995) produced a very similar result for the bulk motion.

The global Hubble flow linearity demonstrated by Lauer & Postman (1992) suggests that that the BCG Lm-alpha relation is an excellent DI out to substantial redshifts. However, the indicated bulk motion is of sufficient amplitude and scale as to appear inconsistent with other indicators of large-scale homogeneity. For example, Strauss et al. (1995) showed that none of the leading models of structure formation that are consistent with other measures of large-scale power can reproduce an LP94-like result in more than a small fraction of realizations. Furthermore, two recent studies, one using the TF relation (Giovanelli et al. 1996) and one using Type Ia SNe (Riess et al. 1995b), suggest that the bulk motion on smaller scales than that probed by the BCGs is inconsistent with the LP94 bulk flow at high significance levels.

For the above reasons, the current status of BCGs as DIs is controversial. However, one should not prejudge the outcome. Velocity studies have yielded a number of surprises in the last 15 years, and it is not inconceivable that the LP94 bulk flow - or something like it - will be vindicated in the long term. Lauer, Postman, and Strauss are currently extending BCG observations to a complete sample with z leq 0.1, and the results of their survey are expected to be available by ~ late 1997. Whether or not it confirms LP94, this extended study is likely to greatly clarify the nature of the BCG Lm-alpha relation.

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