Distribution of τ_max vs. energy including systematic errors as flux biases. green circles: identical to the curve in Fig. 8, following Eq. (1); red triangles: same as above, but with a systematic error of 10% added to the Fermi-LAT spectrum (cf. Sect. 3.1); blue open circles: statistical errors from Fermi-LAT and H.E.S.S. are included using the exact solution derived here, systematic errors have been added to both fluxes as well.