3 2009 Fermi Symposium, Washington, D.C., Nov. 2-5 ulus of the magnetic field roughly constant in each of them. We take, however, randomly chosen orienta- tions, which in practice is also equivalent to a variation in the strength of the component of the magnetic field involved in the photon/axion mixing[31]. Moreover, it will be necessary to include the effect of the Ex- tragalactic Background Light (EBL) in the equations as well, its main effect being an additional attenua- tion of the photon flux, especially at energies above 100 GeV. Indeed, the EBL plays a crucial role to cor- rectly evaluate and understand the importance of the intergalactic mixing. The induced effect can be an attenuation or an enhancement of the photon flux at Earth, depending on distance, magnetic field and the EBL model considered (see next Section). In conclusion, AGNs located at cosmological dis- tances will be affected by both mixing in the source and in the IGMF. As already mentioned, up to now previous works have focused only in studying the pho- ton/axion mixing either inside the source or in the IGMFs. Instead, for the first time we carried out a detailed study of the mixing in both regimes under the same consistent framework. In order to observe both effects in the gamma-ray band, we need ultra-light ALPs. That is the reason why in our fiducial model, presented in Table I, we use a value of m$_{a}$ = 10 − 10 eV, which implies E$_{crit}$ ∼ 30 GeV for the IGMF mixing (for B ∼ 0.1 nG) and E$_{crit}$ ∼ 1 eV within the source and its vicinity (B ∼ 1 G). Consequently, both effects need to be taken into account. We show in Fig. 2 a diagram that outlines our formalism. Very sque- matically, the diagram shows the travel of a photon from the source to the Earth in a scenario with ALPs. In the same Figure, we show the main physical cases that one could identify inside our formalism: mixing in both the source and the IGMF, mixing in only one of these environments, the effect of the EBL, etc. occur in the source and its vicinity. Assuming a mid- value of B ∼ 0.1 nG, and M 11 = 0 . 114 (CAST upper limit), the effect could be observationally detectable by current IACTs ( E$_{crit}$ < 1 TeV) only if the ALP mass is m$_{a}$ < 6 × 10 − 10 eV, i.e. we need ultra-light ALPs. For example, we get E$_{crit}$ = 28 . 5 GeV when using m$_{a}$ = 10 − 10 eV, which is the value given in Ta- ble I as our reference one. 0.01 0.10 1.00 10.00 100.00 1000.00 E (GeV) 0.7 0.8 0.9 1.0 1.1 Intensity FIG. 1: Example of photon/axion oscillations inside the source or vicinity, and its effect on the source intensity (solid line), which was normalized to 1 in the Figure. We used the parameters given in Table I to model the AGN source, but we adopted an ALP mass of 1 µ eV. This gives E$_{crit}$ = 0 . 19 GeV. The dot-dashed line represents the max- imum (theoretical) attenuation, i.e. 1/3. C. Source and intergalactic mixings working together II. AXION BOOSTS TABLE I: Parameters used to calculate the total pho- ton/axion conversion in both the source (for the two AGNs considered, 3C 279 and PKS 2155-304) and in the IGM. The values related to 3C 279 were obtained from Ref. [17], while those ones for PKS 2155-304 were obtained from Ref. [18]. This Table represents our fiducial model. Parameter 3C 279 PKS 2155-304 B (G) 1.5 0.1 Source e d (cm − $^{3}$) 25 160 parameters L domains (pc) 0.003 3 × 10 − 4 B region (pc) 0.03 0.003 z 0.536 0.117 Intergalactic e d,int (cm − $^{3}$) 10 − 7 10 − 7 parameters B int (nG) 0.1 0.1 L domains (Mpc) 1 1 ALP M (GeV) 1.14 × 10 1.14 × 10 parameters ALP mass (eV) 10 − 10 10 − 10 Since we expect the intergalactic mixing to be more important for larger distances, due to the more promi- nent role of the EBL, we chose two distant astrophysi- cal sources as our benchmark AGNs: the radio quasar 3C 279 (z=0.536) and the BL Lac PKS 2155-304 at z=0.117. We summarize in Table I the parameters we have considered in order to calculate the total pho- ton/axion conversion in both the source and in the intergalactic medium. As for the EBL model, we chose the Primack [19] and Kneiske best-fit [20] ones. They represent respectively one of the most transparent and In our model, we assume that the photon beam propagates over N domains of a given length, the mod- eConf C091122