The Galaxy Cluster Mid-Infrared Luminosity Function at 1.3<z<3.2

We present 4.5 {\mu}m luminosity functions for galaxies identified in 178 candidate galaxy clusters at 1.3 < z < 3.2. The clusters were identified as Spitzer/IRAC color-selected overdensities in the Clusters Around Radio-Loud AGN (CARLA) project, which imaged 421 powerful radio-loud AGN at z > 1.3. The luminosity functions are derived for different redshift and richness bins, and the IRAC imaging reaches depths of m*+2, allowing us to measure the faint end slopes of the luminosity functions. We find that {\alpha} = -1 describes the luminosity function very well in all redshifts bins and does not evolve significantly. This provides evidence that the rate at which the low mass galaxy population grows through star formation, gets quenched and is replenished by in-falling field galaxies does not have a major net effect on the shape of the luminosity function. Our measurements for m* are consistent with passive evolution models and high formation redshifts z_f ~ 3. We find a slight trend towards fainter m* for the richest clusters, implying that the most massive clusters in our sample could contain older stellar populations, yet another example of cosmic downsizing. Modelling shows that a contribution of a star-forming population of up to 40% cannot be ruled out. This value, found from our targeted survey, is significantly lower than the values found for slightly lower redshift, z ~ 1, clusters found in wide-field surveys. The results are consistent with cosmic downsizing, as the clusters studied here were all found in the vicinity of radio-loud AGNs -- which have proven to be preferentially located in massive dark matter halos in the richest environments at high redshift -- they may therefore be older and more evolved systems than the general protocluster population.