Hierarchical clustering and the Butcher–Oemler effect

We show that the rapid evolution in the fraction of blue, star-forminggalaxies seen in clusters as a function of redshift (the Butcher-Oemler effect)can be explained very simply if structure formation in the universe proceeedshierarchically. We show that a rich cluster observed at high redshift has had asignificantly different evolutionary history to a cluster of the same richnessobserved today. High redshift clusters take longer to assemble and thus under-go more merging at small lookback times. We have investigated two models ofstar formation in cluster galaxies: 1) a model in which star formation isinduced by galaxy-galaxy mergers and interactions and 2) a model in which starformation is regulated by the infall of galaxies onto larger systems such asgroups and clusters. Both models produce trends consistent with the Butcher-Oemler effect. Our models of cluster formation and evolution allow us to makepredictions about trends in the observed properties of clusters with redshift.We find that there should be a correlation between the mass of the cluster orgroup and the strength of the observed Butcher-Oemler effect, with more massivesystems exhibiting more evolution than less massive systems. We also predictthat both the blue galaxy fraction and the incidence of interacting galaxies inrich clusters should rise continuously with redshift. Finally, we have exploredthe influence of cosmological parameters on our predictions for clusterevolution. We find that models in which structure formation occurs at veryearly epochs, such as low $\Omega$ models, predict rather little recent starformation and merging activity in clusters at redshifts of around 0.4.Comment: Latex file, 12 pages, postscript figures on reques