Results from the simulation of the temporal evolution of a rarefied ionization front. Top panel: temporal evolution of the ionization front. The evolution of the ionization front position (in units of R_S; see Eq. (30)) computed by ATES is represented by the black crosses, and compared to the analytical solution (see Eq. (29)), shown by the solid blue line. Bottom panel: the ionization front temperature profiles are shown at different times, as a function of the distance from the central star.