Dependence of the bright end of composite galaxy luminosity functions on cluster dynamical states

The 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 the Sloan Digital Sky Survey, we obtain the bright end of composite luminosity functions of cluster galaxies, and study their dependence on a cluster dynamical states. 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_*), and these clusters have fewer bright non-BCG member galaxies but a brighter BCG. Our results suggest the co-evolution of galaxy population with a cluster dynamical state and support the hierarchical formation scenario of the BCGs.