Annu. Rev. Astron. Astrophys. 2001. 39: 249-307 Copyright © 2001 by Annual Reviews. All rights reserved

4.4. Interaction with High Energy -Rays

As discussed in Section 3.7, the CIB strongly attenuates -rays from 1-100 TeV. Since the cross section for the - reaction varies strongly with energy near the peak, ~ 50% of the total cross section for 17 TeV photons arises from interactions with 40 to 80 µm background photons (Guy et al. 2000). If I = 28 nW m^-2 sr^-1 at 60 µm, as claimed by Finkbeiner et al. (2000), then the mean free path for 17 TeV photons would be ~ 14 Mpc. This is considerably smaller than the distance to Mrk 501 (160 Mpc for h = 0.65), which would imply that the intrinsic 17 TeV flux from Mrk 501 is larger than the observed flux by a factor of exp(~ 12) 10⁵. This leads to an excessive power output for that galaxy, a situation described by Protheroe & Meyer (2000) as "an infrared background-TeV -ray crisis."

Several possible solutions have been suggested to resolve this "crisis". (a) Harwit et al. (1999) suggested that the actual flux of 10 to 20 TeV photons could be much lower than inferred from the observations. This could occur if lower-energy photons were to arrive coherently, simulating the effect of single 10 to 20 TeV photons with the sum of their energies. (b) Kifune (1999) noted that because the photon energy-momentum relation violates Lorentz invariance in quantum gravity scenarios (Amelino-Camelia et al. 1998, and references therein), the energy threshold for electron pair production can be raised, thus reducing the opacity of the universe to TeV photons by orders of magnitude. (c) The most obvious solution to the crisis is, of course, to assume that most of the 60 and 100 µm radiation tentatively identified as the CIB by Finkbeiner et al. (2000) actually arises from foreground sources.

The opacity of the universe to TeV -rays as a function of -ray energy and source redshift has been calculated using conventional physics by several authors (Primack et al. 1999, Salamon & Stecker 1998, Biller et al. 1998). Photons arriving from distant -ray sources traverse different intergalactic radiation fields at different redshifts. Primack et al. used semianalytical models (Section 5.2.3) to calculate the evolution of the EBL with redshift, whereas Salamon & Stecker calculated these evolutionary effects in the framework of the Fall et al. (1996) cosmic chemical evolution model (Section 5.2.4). For local sources, z << 1, the opacity can be calculated from the local EBL (Coppi & Aharonian 1999, Protheroe & Meyer 2000). Figure 6 presents the opacity of the local universe for TeV -rays implied by the EBL measurements summarized in Figure 5. Figure 6 suggests that the uncertainties in the EBL are sufficiently large that the detection of 10 to 20 TeV -rays does not yet constitute a crisis and that 30 TeV sources could potentially be visible up to a distance of ~ 100 h^-1 Mpc.

Figure 6. Limits for the TeV -ray optical depth, , as a function of -ray energy. The optical depth limits were derived from the EBL limits defined by the shaded area in Figure 5. The optical depth was calculated for H0 = 100 km s-1 Mpc-1 ( H0-1), and a source distance of z = 0.03.