Active galactic nuclei (AGN) can produce both gamma rays and cosmic rays. The observed high-energy gamma-ray signals from distant blazars may be dominated by secondary gamma rays produced along the line of sight by the interactions of cosmic-ray protons with background photons. This explains the surprisingly low attenuation observed for distant blazars, because the production of secondary gamma rays occurs, on average, much closer to Earth than the distance to the source. Thus the observed spectrum in the TeV range does not depend on the intrinsic gamma-ray spectrum, while it depends on the output of the source in cosmic rays. We apply this hypothesis to a number of sources and, in every case, we obtain an excellent fit, strengthening the interpretation of the observed spectra as being due to secondary gamma rays. We explore the ramifications of this interpretation for limits on the extragalactic background light and for the production of cosmic rays in AGN. We also make predictions for the neutrino signals, which can help probe acceleration of cosmic rays in AGN.
Active galactic nuclei (AGN) are believed to produce both gamma rays and cosmic rays. Gamma-ray photons with energies in the TeV range have been observed from a number of distant blazars (Aharonian et al. 2006;Albert et al. 2006;Aharonian et al. 2007a; The identification of observed gamma rays with secondary showers along the line of sight reconciles the observed TeV spectra with theoretical models. The primary gamma rays should exhibit clear signatures of absorption due to their interactions with extragalactic background light (EBL), such as a sharp cutoff at energies around 1 TeV that was predicted prior to observations (Stecker et al. 1992). However, the observed spectra do not show such features (Aharonian et al. 2006;Acciari et al. 2009;Costamante et al. 2008). This can be explained by the lower levels of EBL (Aharonian et al. 2006;Mazin & Raue 2007;Finke & Razzaque 2009), combined with much harder intrinsic spectra of distant blazars (Stecker et al. 2007) than those predicted by earlier models (Peacock 1981;Kirk & Schneider 1987;Heavens & Drury 1988;Bednarz & Ostrowski 1998;Malkov & Drury 2001). Alternatively, the lack of absorption features can be explained by the production of secondary gamma rays, which replace the primary gamma-rays lost to their interactions with EBL (Essey & Kusenko 2010;Essey et al. 2010b). We will present additional evidence that the latter approach provides a consistent explanation of all the present data.
Secondary gamma rays produce point images as long as the magnetic deflections of protons are sufficiently small. The magnetic fields in the source host galaxy introduce only a negligible image broadening, at most, of the order of the galaxy size divided by the distance to the source. In intergalactic space, the magnetic fields are much weaker than inside a galaxy, and can have the field strenghths as low as a femtogauss (Ando & Kusenko 2010;Kandus et al. 2010). Therefore, the proton deflections are small, and the images of sources in secondary photons appear pointlike. Indeed, the deflections of protons emitted by a distant blazar on their passage in a random magnetic field below 10 fG are smaller than the angular resolution of atmospheric Cherenkov telescopes (ACT):
Here D is the distance to the source D and l c is the average correlation length.
It is easy to understand qualitatively why, for a sufficiently distant source, secondary gamma-ray flux should dominate over primary gamma-ray flux. The flux of the primary gamma rays is attenuated by their interactions with EBL and, for a source at distance d, the flux of unattenuated high-energy gamma rays is
where λ γ is the attenuation length due to the interactions with EBL. Cosmic rays emitted from the same source with energies below the GZK cutoff (Greisen 1966;Zatsepin & Kuzmin 1966) of about 3 × 10 10 GeV can cross cosmological distances without a significant energy loss. Their flux at distance d is F protons ∝ 1/d 2 . Although the photon background is optically thin for cosmic rays, the protons do rarely interact with the cosmic background photons and produce gamma rays.
Let us consider an isotropic source of protons. Since the proton flux is not attenuated, the same number of protons pass through every spherical shell at any radius r. Let protons produce gamma rays at the rate p per unit length of path, and the number of gamma rays passing through a shell at distance r is Φ γ (r). Some gamma rays are lost to pair production characterized by attenuation length λ γ . The change in the number of photons Φ γ that occurs between r and r + dr is dΦ γ = p dr -(1/λ γ )Φ γ dr. The solution of this equation with a boundary condition Φ γ (0) = 0, appropriate for secondary gamma rays, is
This derivation extends to beamed sources, as long as the effects of the beam broadening are small, which is the case for IGMF below 10 fG, in agreement with observational data (Kandus et al. 2010).
It is clear from Eqns. (2-3) that, for a sufficiently high proton flux, secondary gamma rays should dominate the spectra of very distant sources above E ∼TeV, because their flux suppression is less severe at large distances.
Secondary neutrinos also show a different scaling with distance. This can be used as a tool to distinguish between primary neutrinos from AGN (Stecker et al. 1991) and secondary neutrinos produced along the line of sight (Essey et al. 2010b). For neutrinos, there is no absorption, and the flux of secondary neutrinos scales as
The 1/d scaling applies as long as the intergalactic magnetic fields (IGMF) are sufficiently small to allow the protons to remain within the angular resolution of the detector. This unique scaling law can be exploited by future experiments: a larger number of sources should be within the field of view than one would predict based on the primary gamma-ray flux.
The secondary gamma rays should arrive at random times and show no temporal variability, and this is consistent with the data. While variabilit
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