Diffuse neutrino intensity from the inner jets of active galactic nuclei: Impacts of external photon fields and the blazar sequence

We study high-energy neutrino production in inner jets of radio-loud active galactic nuclei (AGN), taking into account effects of external photon fields and the blazar sequence. We show that the resulting diffuse neutrino intensity is dominated by quasar-hosted blazars, in particular, flat spectrum radio quasars, and that PeV-EeV neutrino production due to photohadronic interactions with broadline and dust radiation is unavoidable if the AGN inner jets are ultrahigh-energy cosmic-ray (UHECR) sources. Their neutrino spectrum has a cutoff feature around PeV energies since target photons are due to $\mathrm{Ly}\alpha$ emission. Because of infrared photons provided by the dust torus, neutrino spectra above PeV energies are too hard to be consistent with the IceCube data unless the proton spectral index is steeper than 2.5, or the maximum proton energy is $\lesssim 100\mathrm{PeV}$. Thus, the simple model has difficulty in explaining the IceCube data. For the cumulative neutrino intensity from blazars to exceed $\sim {10}^{-8}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$, their local cosmic-ray energy generation rate would be $\sim 10–100$ times larger than the local UHECR emissivity but is comparable to the averaged $\gamma$-ray blazar emissivity. Interestingly, future detectors such as the Askaryan Radio Array can detect $\sim 0.1–1\mathrm{EeV}$ neutrinos even in more conservative cases, allowing us to indirectly test the hypothesis that UHECRs are produced in the inner jets. We find that the diffuse neutrino intensity from radio-loud AGN is dominated by blazars with $\gamma$-ray luminosity of $\gtrsim 10^{48}\mathrm{erg}{\mathrm{s}}^{-1}$, and the arrival directions of their $\sim 1–100\mathrm{PeV}$ neutrinos correlate with the luminous blazars detected by Fermi.

Figure 1

Schematic picture of a blazar, showing external radiation fields relevant for neutrino production.

Figure 2

Continuum blazar SED emission components considered in this work. The sold, dotted, and dashed curves represent the nonthermal continuum jet radiation, the accretion-disk radiation, and the IR radiation from the dust torus, respectively. From top to bottom, the radio luminosity at 5 GHz is given by $\log (L_{5\mathrm{GHz}})=47$, 46, 45, 44, 43, 42, and 41, in units of $\mathrm{erg}{\mathrm{s}}^{-1}$.

Figure 3

Example of energy spectra of target photons in the comoving jet frame for a blob with $\mathrm{\Gamma }=10$, $\delta t^{\prime }={10}^5\mathrm{s}$, and $L_{5\mathrm{GHz}}={10}^{45}\mathrm{erg}{\mathrm{s}}^{-1}$. Broadline emission is plotted assuming $\mathrm{\Delta }\log ϵ=0.1$.

Figure 4

Target photon density in the comoving frame of the blob. Here we assume that $\mathrm{\Gamma }=10$ and $\delta t^{\prime }={10}^5\mathrm{s}$. The broadline emission is plotted with $\mathrm{\Delta }\log ϵ=0.1$, but its detailed shape does not affect calculations of neutrino spectra. The legend gives the 5 GHz radio luminosity $L_{5\mathrm{GHz}}$ in units of $\text{erg}{\mathrm{s}}^{-1}$.

Figure 5

Proton cooling, acceleration, and dynamical time scales in the jet comoving frame. Legend labels the different time scales, including the case of luminous QHBs with $L_{5\mathrm{GHz}}={10}^{47}\mathrm{erg}{\mathrm{s}}^{-1}$ that corresponds to $L_{\text{rad}}={10}^{50.92}\mathrm{erg}{\mathrm{s}}^{-1}$. Note that ${ϵ}_p$ is defined in the comoving frame of the blob and $\mathrm{\Gamma }=10$ is assumed.

Figure 6

Same as Fig. 5, but for QHBs with $L_{5\mathrm{GHz}}={10}^{45}\mathrm{erg}{\mathrm{s}}^{-1}$, corresponding to $L_{\text{rad}}={10}^{49.11}\mathrm{erg}{\mathrm{s}}^{-1}$.

Figure 7

Same as Fig. 5, but for LSP BL Lac objects with $L_{5\mathrm{GHz}}={10}^{43}\mathrm{erg}{\mathrm{s}}^{-1}$, corresponding to $L_{\text{rad}}={10}^{46.56}\mathrm{erg}{\mathrm{s}}^{-1}$.

Figure 8

The same as Fig. 5, but for HSP BL Lac objects with $L_{5\mathrm{GHz}}={10}^{41}\mathrm{erg}{\mathrm{s}}^{-1}$, corresponding to $L_{\text{rad}}={10}^{45.8}\mathrm{erg}{\mathrm{s}}^{-1}$.

Figure 9

Differential luminosity spectra of neutrinos produced in the blazar zone (dotted) and in the BLR and dust torus (solid). The muon neutrino spectrum is calculated for $s=2.3$ and ${\xi }_{\text{cr}}=100$, with neutrino mixing taken into account. From top to bottom, the curves refer to blazar sequence parameters given in Table 1 (see also Fig. 2), with the top curve corresponding to $L_{5\mathrm{GHz}}=10^{47}\mathrm{erg}{\mathrm{s}}^{-1}$. Only five curves are shown for the BLR/dust torus because blazars with the lowest luminosities lack interactions with BLR and dust emission.

Figure 10

Same as Fig. 9, except with $s=2.0$ and ${\xi }_{\text{cr}}=10$.

Figure 11

Effective optical depth to the photohadronic process (thick) and Bethe–Heitler pair production process (thin) for CR protons propagating in the BLR.

Figure 12

Same as Fig. 11 for CR protons propagating in the dust torus.

Figure 13

Cumulative neutrino background from radio-loud AGN in the blazar sequence model. The CR spectral index $s=2.3$, and the CR loading factor ${\xi }_{\text{cr}}=100$ (thick) and 500 (thin). Note that the former value is motivated by the AGN-UHECR hypothesis, where the CR energy injection rate is normalized by the observed UHECR energy generation rate. The atmospheric muon neutrino background is also shown (dotted dashed).

Figure 14

Same as Fig. 13, but for $s=2.0$. Here ${\xi }_{\text{cr}}=3$ (thick), and ${\xi }_{\text{cr}}=50$ (thin). Note that the former value is motivated by the AGN-UHECR hypothesis.

Figure 15

Cumulative neutrino background from radio-loud AGN for $s=2.3$ and ${\xi }_{\text{cr}}=100$. Contributions from blazars with different $\gamma$-ray luminosity thresholds, as given by the legend, are shown. Neutrino emission by external radiation from the BLR and dust torus is shown.

Figure 16

Same as Fig. 15, but neutrino emission from the blazar zone is shown.