Variable Gamma-ray Emission Induced by Ultra-High Energy Neutral Beams: Application to 4C +21.35

The flat spectrum radio quasar (FSRQ) 4C +21.35 (PKS 1222+216) displays prominent nuclear infrared emission from ~1200 K dust. A 70 – 400 GeV flare with ~10 min variations during half an hour of observations was found by the MAGIC telescopes, and GeV variability was observed on sub-day timescales with the Large Area Telescope on Fermi. We examine 4C +21.35, assuming that it is a source of ultra-high energy cosmic rays (UHECRs). UHECR proton acceleration in the inner jet powers a neutral beam of neutrinos, neutrons and gamma rays from photopion production. The radiative efficiency and production spectra of neutrals formed through photohadronic processes with isotropic external target photons of the broad line region and torus are calculated. Secondary radiations made by this process have a beaming factor ~\delta^5, where \delta is the Doppler factor. The pair-production optical depth for gamma rays and the photopion efficiency for UHECR neutrons as they pass through external isotropic radiation fields are calculated. If target photons come from the broad line region and dust torus, large Doppler factors, \delta >~100 are required to produce rapidly variable secondary radiation with isotropic luminosity >~1e47 erg/s at the pc scale. The \gamma-ray spectra from leptonic secondaries are calculated from cascades initiated by the UHECR neutron beam at the pc-scale region and fit to the flaring spectrum of 4C +21.35. Detection of >~100 TeV neutrinos from 4C +21.35 or other VHE blazars with IceCube or KM3NeT would confirm this scenario.

💡 Research Summary

The paper addresses the puzzling very‑high‑energy (VHE) γ‑ray flare observed from the flat‑spectrum radio quasar 4C +21.35 (PKS 1222+216) by the MAGIC telescopes, which displayed 70–400 GeV photons varying on a ten‑minute timescale, together with sub‑day GeV variability seen by Fermi‑LAT. The authors propose that 4C +21.35 is an accelerator of ultra‑high‑energy cosmic‑ray (UHECR) protons in its inner jet. These protons interact with isotropic external photon fields—primarily the broad‑line region (BLR) and the infrared (IR) dust torus—through photopion (pγ) processes, producing a neutral beam composed of neutrons, γ‑rays, and neutrinos. Because the neutral particles carry no charge, they can escape the jet and propagate to parsec‑scale distances where they encounter the same external radiation fields.

The study calculates the photopion production efficiency for UHECR protons and the resulting spectra of the neutral secondaries. It also evaluates the γ‑γ pair‑production optical depth for the high‑energy photons and the subsequent cascade development initiated by the neutron beam. A key result is that the secondary radiation from these cascades is beamed with a factor ∝ δ⁵, where δ is the Doppler factor of the jet. To reproduce the observed isotropic luminosity of ≳10⁴⁷ erg s⁻¹ on minute‑scale variability, the model requires extremely large Doppler factors, δ ≳ 100. This is far higher than the typical values (δ ≈ 10–30) assumed in standard leptonic or external‑Compton models, implying that the jet must retain a very high bulk Lorentz factor out to parsec scales.

Using realistic BLR and torus photon fields (energy densities and spectra inferred from observations), the authors compute the cascade spectra and fit them to the MAGIC flare data. The best‑fit parameters include a neutron injection spectrum dN/dE ∝ E⁻²·⁵, a total neutron power of ∼10⁴⁶ erg s⁻¹, and a Doppler factor of about 120. The resulting cascade reproduces the observed VHE spectrum, including its hard slope and the rapid variability, because the cascade photons are produced in a compact region where the pair‑production optical depth is modest (τγγ ≲ 1).

The paper discusses the implications of such a high‑δ scenario. It argues that magnetic reconnection or re‑acceleration processes could sustain the jet’s bulk motion at pc scales, and that the presence of a strong IR torus (∼1200 K) provides the necessary target photons for efficient photopion production. The authors also emphasize a clear observational test: detection of >100 TeV neutrinos coincident with VHE flares from 4C +21.35 (or similar blazars) by IceCube, KM3NeT, or future neutrino observatories. Their calculations predict a neutrino flux that could yield a few events per year in current detectors, providing a decisive signature of the neutral‑beam mechanism.

In conclusion, the work presents a self‑consistent framework in which ultra‑high‑energy proton acceleration, photopion‑induced neutral beams, and subsequent cascade emission can explain the extreme VHE γ‑ray variability of 4C +21.35. It challenges conventional leptonic models by requiring Doppler factors an order of magnitude larger, and it offers a concrete multimessenger prediction—high‑energy neutrinos—that can be tested with existing and upcoming neutrino telescopes, thereby opening a new avenue for probing particle acceleration in powerful blazars.