Distribution functions for clusters of galaxies from N-body simulations

We present the results of an attempt to adapt the distribution function formalism to characterize large-scale structures like clusters of galaxies that form in a cosmological N-body simulation. While galaxy clusters are systems that are not strictly in equilibrium, we show that their evolution can nevertheless be studied using a physically motivated extension of the language of equilibrium stellar dynamics. Restricting our analysis to the virialized region, a prescription to limit the accessible phase-space is presented, which permits the construction of both the isotropic and the anisotropic distribution functions $f(E)$ and $f(E,L)$. The method is applied to models extracted from a catalogue of simulated clusters. Clusters evolved in open and flat background cosmologies are followed during the course of their evolution, and are found to transit through a sequence of what we define as `quasi-equilibrium' states. An interesting feature is that the computed $f(E)$ is well fit by an exponential form. We conclude that the dynamical evolution of a cluster, undergoing relaxation punctuated by interactions and violent mergers with consequent energy-exchange, can be studied both in a qualitative and quantitative fashion by following the time evolution of $f(E)$.

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