Density (top panel) and velocity (bottom panel) fields of the solutions for various values of σ. For values of X smaller than the position of the shock (X<X_sh ≃ 3), the density and the velocity are unperturbed, i.e. δR = δV = 0. The solid lines show the solutions for the system of Eqs. (5)–(7) For comparison, solutions to the same equations but without the thermal pressure term are shown with the dotted lines.