Self‐similar Spherical Collapse Revisited: A Comparison between Gas and Dark Matter Dynamics

Abstract

We reconsider the collapse of cosmic structures in an Einsteinde Sitter universe, using the self-similar initial conditions of Fillmore & Goldreich (1984). We rst derive a new approximation to describe the dark matter dynamics in spherical geometry, which we refer to as the "" uid approach. This method enables us to recover the self-similarity solutions of Fillmore and Goldreich for dark matter. We also derive new self-similarity solutions for the gas. We thus compare directly gas and dark matter dynamics, focusing on the di erences due to their di erent dimensionalities in velocity space. This work may have interesting consequences for gas and dark matter distributions in large galaxy clusters, allowing us to explain why the total mass prole is always steeper than the X-ray gas prole. We also discuss the shape of the dark matter density prole found in N-body simulations in terms of a change of dimensionality in the dark matter velocity space. The stable clustering hypothesis has been nally considered in light of this analytical approach.