Surface brightness along the line of sight to the limb of a non-relativistic shock as a function of distance x to the shock, for various cases as shown: upper panel at hν = 1 keV, lower panel at hν = 10 keV. The solid lines present a complete numerical evaluation of Eq. (15), while the dotted lines correspond to the analytical approximation in the turn-over regime. Two models are shown for the precursor emission: α_λ = 1 for the upper lines, i.e. t_scatt ∝ p^1/2, and α_λ = 0 for the lower lines, i.e. Bohm scaling t_scatt ∝ p. In all cases, β_sh = 1/30, n_u = 1 cm^-3, R = 1 pc, ϵ_Bp = 0.001, and ϵ_e = 0.01.