The K_s-band luminosity and stellar mass functions of galaxies in z ∼ 1 clusters

We present the near-infrared (K_s-band) luminosity function of galaxies in two z ∼ 1 cluster candidates, 3C 336 and Q1335+28. A third cluster, 3C 289, was observed but found to be contaminated by a foreground system. Our wide-field imaging data reach to K_s = 20.5 (5σ), corresponding to ∼ M* + 2.7 with respect to passive evolution. The near-infrared luminosity traces the stellar mass of a galaxy due to its small sensitivity to the recent star formation history. Thus the luminosity function can be transformed to the stellar mass function of galaxies using the J - K _s colours with only a small correction (factor ≲2) for the effects of ongoing star formation. The derived stellar mass function spans a wide range in mass from ∼3 × 10¹¹ M_⊙ down to ∼6 × 10⁹ M_⊙ (set by the magnitude limit). The form of the mass function is very similar to lower-redshift counterparts such as that from 2MASS/LCRS clusters (given by Balogh et al.) and the z = 0.31 clusters (given by Barger et al.). This indicates little evolution of galaxy masses from z = 1 to the present day. Combined with colour data suggesting that star formation is completed early (z ≫ 1) in the cluster core, it seems that the galaxy formation processes (both star formation and mass assembly) are strongly accelerated in dense environments and have been largely completed by z = 1. We investigate whether the epoch of mass assembly of massive cluster galaxies is earlier than that predicted by the semi-analytic hierarchical galaxy formation models. These models predict the increase of characteristic mass by more than a factor of ∼3 between z = 1 and the present day. This seems incompatible with our data.