Probability density function of the gas for the three simulations. Left t = 0 ky, middle t = 500 ky, right t = 1 My. The first peak is the ionized gas and therefore not seen in the observations. At t = 500 ky, the Mach-1 simulation presents a double peak, the first one corresponding to the unperturbed turbulent gas, the second one to the shocked region. In the Mach-2 simulations, the peak is barely visible because the turbulence is higher and the unperturbed region still present in the box becomes small. In the Mach-4 simulation, the turbulence is too high, and the second peak is hidden in the peak of the turbulent cold region.