Implications of multiwavelength spectrum on cosmic-ray acceleration in blazar TXS 0506+056

Context. The MAGIC collaboration has recently analyzed data from a long-term multiwavelength campaign of the γ-ray blazar TXS 0506+056. In December 2018 it was flaring in the very high-energy (VHE; E > 100 GeV) γ-ray band, but no simultaneous neutrino event was detected.
Aims: We modeled the observed spectral energy distribution (SED) using a one-zone leptohadronic emission.
Methods: We estimated the neutrino flux through the restriction from the observed X-ray flux on the secondary radiation due to the hadronic cascade, initiated by protons with energy E_p ≲ 0.1 EeV. We assumed that ultra-high-energy cosmic rays (UHECRs; E ≳ 0.1 EeV), with the same slope and normalization as the low-energy spectrum, are accelerated in the jet but escape efficiently. We propagate the UHE protons in a random turbulent extragalactic magnetic field (EGMF).
Results: The leptonic emission from the jet dominates the GeV range, whereas the cascade emission from CR interactions in the jet contributes substantially to the X-ray and VHE range. The line-of-sight cosmogenic γ-rays from UHECRs produce a hardening in the VHE spectrum. Our model prediction for neutrinos from the jet is consistent with the 7.5-year flux limit by IceCube and shows no variability during the MAGIC campaign. Therefore, we infer that the correlation between GeV-TeV γ-rays and neutrino flare is minimal. The luminosity in CRs limits the cosmogenic γ-ray flux, which in turn bounds the RMS value of the EGMF to ≳10⁻⁵ nG. The cosmogenic neutrino flux is lower than the IceCube-Gen2 detection potential for 10 yr of observation.
Conclusions: Very high-energy γ-ray variability should arise from increased activity inside the jet; thus, detecting steady flux at multi-TeV energies may indicate UHECR acceleration. Upcoming γ-ray imaging telescopes, such as the CTA, will be able to constrain the cosmogenic γ-ray component in the SED of TXS 0506+056.