Dependence of the bright end of galaxy luminosity function on cluster
  dynamical state
  Luminosity function of cluster galaxies provides a fundamental constraint on
galaxy evolution in cluster environments. By using the bright member galaxies
of a large sample of rich clusters identified from Sloan Digital Sky Survey, we
obtain the bright end of composite luminosity functions of cluster galaxies,
and study their dependence on cluster dynamical state. After a
redshift-evolution correction of absolute magnitude, the luminosity function of
member galaxies can be well fitted by a Schechter function when the brightest
cluster galaxies (BCGs) are excluded. The absolute magnitudes of BCGs follow a
Gaussian function with a characteristic width of about 0.36 mag. We find that
the luminosity function of galaxies in more relaxed clusters has a fainter
characteristic absolute magnitude (M_{\ast}), and these clusters have fewer
bright non-BCG member galaxies but a brighter BCG. Our results suggest the
co-evolution of galaxy population with cluster dynamical state and somewhat
support the hierarchical formation scenario of the BCGs.
