A WISE view of the composite luminosity function of cluster members
  Galaxy clusters play a crucial role in constraining cosmological parameters.
Cluster detection and characterization have therefore become an important field
of modern cosmology. In this work, we aim at constructing reasonably
representative composite luminosity function of cluster members in the WISE
survey that can be used in the future as an input in matching algorithms for
cluster detection. We use a sample of massive clusters from the redMaPPer
catalog to match the positions of the WISE sources. We build the composite
luminosity function of the WISE members in different redshift bins. We find
that galaxy cluster members have a characteristic composite luminosity
function, with a clear change in the slope at a given magnitude apparent
$M^{*}$, which becomes fainter with increasing redshift. The best-fit
bright-end slope $\beta$ is compatible with a constant value of $3.54$ with no
clear trend with redshift, while the faint-end slope $\alpha$ is remarkably
different, ranging from $2$ to $3$. We present the first characterization of
the composite luminosity function of the WISE counterparts of redMaPPer cluster
members and in this way we provide an element for building cluster detection
techniques based on matching algorithms.
