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one of the most opaque models for gamma-rays, but still within the limits imposed by the observations. 

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In order to quantitatively study the effect of ALPs 

on the total photon intensity, we plot in Figure 3 the difference between the predicted arriving photon in- tensity without including ALPs and that one obtained when including the photon/axion oscillations (called here the axion boost factor ). This was done for our fiducial model (Table I) and for the two EBL mod- els considered. The plots show differences in the ax- ion boost factors obtained for 3C 279 and PKS 2155- 304 due mostly to the redshift difference. The in- ferred critical energies for the mixing in the source are E$_{crit}$ = 4 . 6 eV for 3C 279 and E$_{crit}$ = 69 eV for PKS 2155-304, while for the mixing in the intergalac- tic medium we obtain E$_{crit}$ = 28 . 5 GeV (the same for both objects). For B=0.1 nG, and in the case of 3C 279, the axion boost is an attenuation of about 16% below the critical energy (due to mixing inside the source). Above this critical energy and below 200- 300 GeV, where the EBL attenuation is still small, there is an extra attenuation of about 30% (mixing in the IGMF). Above 200-300 GeV the axion boost reaches very high values: at 1 TeV, a factor of ∼ 7 for the Primack EBL model and ∼ 340 for the Kneiske best-fit model. We find that the more attenuating the EBL model considered, the more relevant the ef- fect of photon/axion oscillations in the IGMF, since any ALP to photon reconversion might substantially enhance the intensity arriving at Earth. In the case of PKS 2155-304, the situation is different from that of 3C 279 due to the very low photon-attenuation at the source and, mostly, due to the smaller source dis- tance. Furthermore, a very interesting result is found when varying the modulus of the intergalactic mag- netic field. Higher B values do not necessarily trans- late into higher photon flux enhancements. There is always a B value that maximizes the axion boost fac- tors; this value is sensitive to the source distance, the considered energy and the EBL adopted model (see Ref. [1] for a detailed discussion on this issue). 

