The abundance and colours of galaxies in high redshift clusters in the
  cold dark matter cosmology
  High-redshift galaxy clusters allow us to examine galaxy formation in extreme
environments. Here we compile data for 15 $z>1$ galaxy clusters to test the
predictions from a state-of-the-art semi-analytical model of galaxy formation.
The model gives a good match to the slope and zero-point of the cluster red
sequence. The model is able to match the cluster galaxy luminosity function at
faint and bright magnitudes, but underestimates the number of galaxies around
the break in the cluster luminosity function. We find that simply assuming a
weaker dust attenuation improves the model predictions for the cluster galaxy
luminosity function, but worsens the predictions for the red sequence at bright
magnitudes. Examination of the properties of the bright cluster galaxies
suggests that the default dust attenuation is large due to these galaxies
having large reservoirs of cold gas as well as small radii. We find that
matching the luminosity function and colours of high-redshift cluster galaxies,
whilst remaining consistent with local observations, poses a challenge for
galaxy formation models.
