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Individual dark matter halos in cosmological simulations vary widely in theirdetailed structural properties such as shape, rotation, substructure and degreeof internal relaxation. Recent non-parametric (principal component) analysessuggest that a few principal components explain a large fraction of the scatterin halo properties. The main principal component is closely linked withconcentration, which in turn is known to be related to the mass accretionhistory of the halo. Here we examine more generally the connection between massaccretion history and structural parameters. The space of mass accretionhistories has principal components of its own. We find that the strongest twocan be interpreted as the overall age of the halo and the acceleration ordeceleration of growth at late times. These two components only account for$\sim70$%\ of the scatter in mass accretions histories however, due to thestochastic effect of major mergers. Relating structural parameters to formationhistory, we find that concentration correlates strongly with the early historyof the halo, while relaxation correlates with the late history. We examine theinferences about formation history that can be drawn by splitting haloes intosubsamples, based on observable properties such as concentration and shape atsome final time. This approach suggests interesting possibilities, such as thepossibility of defining young and old samples of galaxy clusters in a rigorous,quantitative way, or testing the dynamical assumptions of galaxy formationmodels empirically.

What Do Dark Matter Properties Tell Us About Their Mass Assembly Histories?