Abstract
Similarity solutions are found for the adiabatic collapse of density perturbations in a flat universe containing collisional gas only. The solutions are obtained for planar, cylindrical and spherical perturbations with zero initial pressure. For adiabatic index a shock develops at a fixed fraction of the current turnaround distance. Near the centre of a spherical perturbation with and the gas is in quasi-hydrostatic equilibrium (pressure-supported) and has an asymptotic power-law density profile, independent of γ. For the profile depends on γ, the pressure is finite, the temperature decreases inwards, and gravity dominates pressure, causing a continuous inward flow. Although for the temperature decreases at the centre, the gas is pressure-supported. The pressure is finite in cylindrical perturbations for and in planar perturbations for any We also derive the asymptotic behaviour of the gas variables near the centre in a universe dominated by collisionless matter. In such a universe, the gas in a spherical perturbation with cannot be pressure-supported and the temperature approaches a constant near the centre. The solutions and the asymptotic behaviour are relevant for modelling the gas distribution in galaxy clusters and pancake-like superclusters, and for determining the structure of haloes of self-interacting dark matter with large interaction cross-section.
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