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Abstract. Analytical models of the abundance of Dark Matter haloes usually focus on their mean initial overdensity as the parameter that determines where and when virialized regions form. This assumption however leads to a number of inconsistencies and divergencies in the calculation. We argue that a more suitable quantity for this purpose is the initial energy of the protohalo patch. We show how this dynamically motivated choice allows to connect the non-linear evolution of the density field with perturbation theory.
We then explore the generation of velocity dispersion in the multistream regime, numerically and by means of a simple analytical model based on spherical collapse. We show how the initial mean energy is crucial to describe the virialization process and to predict the final density profile.
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