Self-similar cosmological expansion of collisional gas

Abstract

We derive similarity solutions for the expansion of negative initial density perturbations δM/M \propto r^-s (s>0) in an Einstein-de Sitter universe filled with collisional baryonic gas and collisionless matter. The solutions are obtained for planar, cylindrical, and spherical perturbations. For steep perturbations, central cavities surrounded by over-dense shells expanding as t^{2(s+1)/3s} develop in both matter components. We also consider the case when baryonic shells are driven by internal pressure. Before redshift \sim 8-10 baryonic shells cool by inverse Compton scattering with the cosmic background radiation and can form bound objects of mass \sim 10^11Ω_b^{-1/2} M_{\odot} (1+z)^{-3/2}. Hot shocks of radius R cause a Compton y-distortion of order y=10^{-5}Ω_b (R/10 Mpc)^2 f_F, where f_F is the volume filling factor of these shells.