Secondary photons and neutrinos from cosmic rays produced by distant blazars

It was recently pointed out that interactions of cosmic rays emitted by AGN with the photon background along the line of sight can produce γ rays that may have already been observed by the Cherenkov telescopes [2]. The spectra of γ rays observed from distant blazars [3] are readily reproduced by the secondary photons produced in interactions of cosmic rays with the cosmic backgrounds [2]. While there is little doubt that AGN are ample sources of primary γ rays, these primary photons are subject to attenuation at TeV energies due to the pair production losses on the extragalactic background light (EBL). The secondary photons produced by proton-photon interactions nearby can replace the primary photons in the highenergy tails of the spectra observed from the most distant blazars.

This possibility, which is interesting in its own right, has far-reaching implications for both the extragalactic background light (EBL) and intergalactic magnetic fields (IGMF). Indeed, γ-ray observations provide a unique probe of EBL, assuming the signals are pure primary photons, uncontaminated by secondary photons [3][4][5][6][7][8][9]. This assumption may be incorrect since protons emitted by AGN can contribute to γ-ray signals, as evidenced by the γ-ray spectra of several distant blazars that do not show an expected attenuation at energies above TeV. The lack of attenuation could be evidence of a relatively low EBL [7,[9][10][11], very hard emission spectra [3], or of some new physics in the form of axion-like particles [12], or Lorentz invariance violation [4]. A less exotic explanation is that the secondary photons replace primary photons in the high-energy tails of the AGN spectra, hence creating a spectrum without a cutoff that is well fit to AGN at relatively high redshift [2].

In this paper we explore the multi-messenger signals of AGN focusing, in particular, on the neutrinos accompanying the secondary photons. AGN are expected to accelerate cosmic rays to energies up to ∼ 10 11 GeV, but most likely have a high energy cutoff below that [13] due to interactions at the source. Thus we will consider cutoffs in the range 10 8 GeV -10 11 GeV. Cosmic rays with energies below the Greisen-Zatsepin-Kuzmin (GZK) cutoff [14] of about 3 × 10 10 GeV can cross cosmological distances without a significant energy loss. However, with a small probability, these protons do interact with the cosmic backgrounds and produce photons. Our investigation differs form the earlier studies of neutrino signals from AGN [15], which assumed that all the pion production occurs at the source. We will discuss the important differences in the two types of signals: from the hadronic interactions in situ and along the line of sight. We will concentrate on protons with energies below the GZK cutoff, which can travel cosmological distances; we will not discuss the cosmogenic neutrinos produced by protons with energies above the GZK cutoff [16].

The secondary photons are generated in two types of interactions of UHECR along the line of sight. First, the proton interactions with CMB photons can produce electron-positron pairs and give rise to an electromagnetic cascades due to what is called proton pair production (PPP), pγ CMB → pe + e - [17]. Second, proton interactions with the EBL can produce pions, which decay and produce photons as well in the reactions pγ EBL → pπ 0 or pγ EBL → nπ + . While the PPP process is not associated with any neutrinos, the pion photoproduction generates a neutrino flux related to the γ-ray flux. The relative importance of the two processes depends on the proton injection spectrum, which we will parameterize by a constant power-law exponent α and maximal energy E max :

Although the spectral index α = 2.7 +0.05 -0.15 gives a good fit to the UHECR data at the highest energies [18], the measured spectrum is a superposition of individual sources with different values of E max . Thus we consider a smaller value of α ≈ 2, which agrees with the data at lower energies [18]. The parameters α and E max determine the power in the highest-energy cosmic rays, which pile up around the GZK energy and contribute to the PPP process. As for the pion photoproduction on EBL, it is mainly due to the lower part of the proton spectrum, at energies of the order of 10 8 GeV. The predicted spectral shape of secondary photons is not very sensitive to the variations in α and E max ; it is determined primarily by the spectrum of the background photons. The model predictions agree with the data on the most distant sources [2] for an effective luminosity of a single AGN in cosmic rays above 10 7 GeV in the range L eff = (10 47 -10 49 ) erg/s. The observed luminos