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: αλ = 1 for the upper lines, i.e. tscatt ∝ p1/2, and αλ = 0 for the lower lines, i.e. Bohm scaling tscatt ∝ p. In all cases, βsh = 1/30, nu = 1 cm-3, R = 1 pc, ϵBp = 0.001, and ϵe = 0.01.
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