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-.
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) Lm varied roughly linearly with a shape parameter defined by
More recently,
Lauer & Postman (1992)
have shown that the correlation
between Lm and 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-
relation is ~ 16%.
A slight hitch in applying the BCG Lm- relation is the requirement
of defining a metric radius rm for evaluating both
Lm and .
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
( 7000 km s-1)
at which the relation is applied, peculiar velocity
corrections have a small effect on Lm and . Iterative techniques
in which a peculiar velocity solution is
obtained and then used to modify the rms, converge quickly
(Lauer & Postman
1994).
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
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 350°, b
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- 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 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- relation.
Figure 7. Top panel: the BCG Lm- 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.