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 Ep ≲ 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.