Hierarchical clustering and the Butcher–Oemler effect

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Abstract
We show that the rapid evolution in the fraction of blue, star-forming galaxies seen in clusters as a function of redshift (the Butcher–Oemler effect) can be explained very simply if structure formation in the Universe proceeds hierarchically. We show that a rich cluster observed at high redshift has had a significantly different evolutionary history from a cluster of the same richness observed today. High-redshift clusters are assembled over a shorter time interval and undergo more merging in the few Gyr just prior to the epoch at which they are observed. We have investigated two models of star formation in cluster galaxies: (1) a model in which star formation is induced by galaxy-galaxy mergers and interactions, and (2) a model in which star formation is regulated by the infall of galaxies on to larger systems such as groups and clusters. Both models produce trends consistent with the Butcher–Oemler effect. Our models of cluster formation and evolution allow us to make predictions about trends in the observed properties of clusters with redshift. We find that there should be a correlation between the mass of the cluster or group and the strength of the observed Butcher–Oemler effect, with more massive systems exhibiting more evolution than less massive systems. We also predict that both the blue galaxy fraction and the incidence of interacting or merging galaxies in rich clusters should rise continuously with redshift. Finally, we have explored the influence of cosmological parameters on our predictions for cluster evolution. We find that models in which structure formation occurs at very early epochs, such as low-Ω models, predict rather little recent star formation and merging activity in clusters at redshifts around 0.4. Detailed comparison with the observations is presented in a companion paper.
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