The luminosities of the brightest cluster galaxies and brightest
  satellites in SDSS groups
  We show that the distribution of luminosities of Brightest Cluster Galaxies
in an SDSS-based group catalog suggests that BCG luminosities are just the
statistical extremes of the group galaxy luminosity function. This latter
happens to be very well approximated by the all-galaxy luminosity function
(restricted to Mr<-19.9), provided one uses a parametrization of this function
that is accurate at the bright end. A similar analysis of the luminosity
distribution of the Brightest Satellite Galaxies suggests that they are best
thought of as being the second brightest pick from the same luminosity
distribution of which BCGs are the brightest. I.e., BSGs are not the brightest
of some universal satellite luminosity function, in contrast to what Halo Model
analyses of the luminosity dependence of clustering suggest. However, we then
use mark correlations to provide a novel test of these order statistics,
showing that the hypothesis of a universal luminosity function (i.e. no halo
mass dependence) from which the BCGs and BSGs are drawn is incompatible with
the data, despite the fact that there was no hint of this in the BCG and BSG
luminosity distributions themselves. We also discuss why, since extreme value
statistics are explicitly a function of the number of draws, the consistency of
BCG luminosities with extreme value statistics is most clearly seen if one is
careful to perform the test at fixed group richness N. Tests at, e.g., fixed
total group luminosity Ltot, will generally be biased and may lead to erroneous
conclusions.
