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

The flat-spectrum radio quasar 4C +21.35 (PKS 1222+216) displays prominent nuclear infrared emission from ≈1200 K dust. A 70-400 GeV flare with ≈10 minute 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 γ-rays from pγ photopion production. The radiative efficiency and production spectra of neutrals formed through photohadronic processes with isotropic external target photons of the broad-line region (BLR) and torus are calculated. Secondary radiations made by this process have a beaming factor vpropδ⁵ _D, where δ_D is the Doppler factor. The pair-production optical depth for γ-rays and the photopion efficiency for UHECR neutrons as they pass through external isotropic radiation fields are calculated. If target photons come from the BLR and dust torus, large Doppler factors, δ_D >~ 100, are required to produce rapidly variable secondary radiation with isotropic luminosity >~ 10⁴⁷ erg s^-1 at the pc scale. The γ-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 very high energy γ-ray blazars with IceCube or KM3NeT would confirm this scenario.