Constraints on the merging time-scale of luminous red galaxies, or, where do all the haloes go?

In the Λ cold dark matter cosmology, dark matter haloes grow primarily through the accretion of smaller haloes. Much of the mass in a halo of 1014 M⊙ comes in through accretion of ∼1013 M⊙ haloes. If each such halo hosted one luminous red galaxy (LRG) then the accretion of so many haloes is at odds with the observed number of LRGs in clusters unless these accreted LRGs merge or disrupt on relatively short time-scales (∼2 Gyr). These time-scales are consistent with classical dynamical friction arguments, and imply that two to three LRGs have merged or disrupted within each halo more massive than 1014 M⊙ by z= 0. The total amount of stellar mass brought into these massive haloes by z= 0 is consistent with observations once the intracluster light (ICL) is included. If disrupted LRGs build up the ICL, then the hierarchical growth of massive haloes implies that a substantial amount of ICL should also surround satellite LRGs, as suggested by recent observations of the Virgo cluster. Finally, we point out that these results are entirely consistent with a non-evolving clustering strength and halo occupation distribution, and note that observations of the latter in fact support the hypothesis that merging/disruption of massive galaxies does indeed take place at late times.