B.S. DISSERTATION:

Pontificia Universidad Católica de Chile (PUC)
January 1999, Santiago, Chile

Author: Ricardo Demarco
Advisor: Prof. A. Reisenegger (PUC)

Self-similar Solutions for the Spherical Collapse of Gas in an Einstein-de Sitter Universe

ABSTRACT:   We study the collapse of gas in the universe to form structures and we search for self-similar solutions to describe the density (ρ), velocity (v) and pressure (p) distributions of the gas. For simplicity, we consider that such a collapse has spherical geometry and that it takes place in a Einstein-de Sitter universe. We also assume that initially the infalling gas has no entropy and we neglect any angular momentum of the system. After reaching the corresponding turnaround radius, the gas layers will collapse towards the center of the growing structure, forming at some radius a shock front that will propagate outwards. The Hugoniot-Rankine relations at the shock are used to find self-similar solutions for the gas density, velocity and pressure distributions in the inner and outer regions of the shock front. For a self-gravitating gas, both the size of the collapsing region and the size of the region inside the shock increase in time as t^κ, with 2/3 < κ < 2. This implies that the solutions near the center are stationary and in hydrostatic equilibrium, with v(r)=0, p(r) ∝ r^n(2/n-2) and ρ(r) ∝ r^-n, where 1 < n < 3. Our results are more general than those obtained by Bertschinger (1985) and provide stronger constraints to the solutions proposed by Fillmore & Goldreich (1984) and Teyssier et al. (1997) in the case of a power-law density profile. However, our solutions are not able to reproduce the constant gas distribution observed in the center of galaxy clusters, suggesting a more complex distribution of the gas than the simple self-similar one of this work. Another possibility is that a non-spherical collapse is the responsible of the central core in the gas distribution of clusters.