Differential luminosity function of the XXL-100-GC sample in the WMAP9 cosmology measured with the cumulative estimator defined by Eq. (7). The effective volume correction derives from the XXL-100-GC scaling relations provided in Table 1. The dashed lines show the predictions of the luminosity function in the WMAP9 cosmological model for the same redshift bins as the measurements, and using the same colour code. Left: differential luminosity function averaged over the full redshift range of [0–1.2] covered by the XXL-100-GC sample, and for the northern/southern field separately. The χ² plot shows how the deviation of each subfield from the complete analysis compares with the combined error bars. Right: differential luminosity function of the bright XXL cluster sample in three redshift bins. The lower plot shows the residuals with respect to the low-redshift WMAP9 prediction.