The galaxy population of Cl 1601+42 at z=0.54

Photometric redshifts are used to determine the rest-frame luminosity function (LF) of both early- and late-type galaxies to  M_B～?17.6  for the cluster Cl 1601+42 at  z=0.54  . The total LF shows a steep faint-end slope   α ～?1.4  , indicating the existence of a population of numerous dwarf galaxies. Luminous galaxies, with  M_B??19.5  are mostly red, early-type galaxies, with a LF best described by a Gaussian. Faint galaxies are predominantly blue, late-type galaxies, well fitted by a Schechter function with   α ～?1.7  . Compared with clusters at lower redshift, the steepening of the faint end starts at brighter magnitudes for Cl 1601+42, which may indicate a brightening of the present-day dwarf population relative to the giant population with increasing redshift. Early-type galaxies are centrally concentrated, and dominate the core region, implying that the radial gradient of early-type galaxies seen in local clusters is already established at  z～0.5  . Bright, late-type galaxies are rare, consistent with a decrease in star formation in field galaxies as they are accreted on to the cluster, while faint, blue galaxies are evenly distributed across the cluster, except for a depletion in the core region. The blue fraction is  f_B～0.15  , which is somewhat lower than the Butcher–Oemler average at  z～0.5  . The value of f _B is found to increase with limiting magnitude and with radius from the centre.