The XXL Survey XXVIII. Galaxy luminosity functions of the XXL-N clusters
  The main goal of this study is to investigate the LF of a sample of 142 X-ray
selected clusters, with spectroscopic redshift confirmation and a well defined
selection function, spanning a wide redshift and mass range, and to test the LF
dependence on cluster global properties, in a homogeneous and unbiased way. Our
study is based on the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)
photometric galaxy catalogue,associated with photometric redshifts. We
constructed LFs inside a scaled radius using a selection in photometric
redshift around the cluster spectroscopic redshift in order to reduce
projection effects. The width of the photometric redshift selection was
carefully determined to avoid biasing the LF and depended on both the cluster
redshift and the galaxy magnitudes. The purity was then enhanced by applying a
precise background subtraction. We constructed composite luminosity functions
(CLFs) by stacking the individual LFs and studied their evolution with redshift
and richness, analysing separately the brightest cluster galaxy (BCG) and
non-BCG members. We fitted the dependences of the CLFs and BCG distributions
parameters with redshift and richness conjointly in order to distinguish
between these two effects. We find that the usual photometric redshift
selection methods can bias the LF estimate if the redshift and magnitude
dependence of the photometric redshift quality is not taken into account. Our
main findings concerning the evolution of the galaxy luminosity distribution
with redshift and richness are that, in the inner region of clusters and in the
redshift-mass range we probe (about $0<z<1$ and $10^{13}
M_{\odot}<M_{500}<5\times10^{14}M_{\odot}$), the bright part of the LF (BCG
excluded) does not depend much on mass or redshift except for its amplitude,
whereas the BCG luminosity increases both with redshift and richness, and its
scatter decreases with redshift.
