We present a procedure to generally constrain the environments of neutrino-producing sites in photomeson production models of jetted Active Galactic Nuclei (AGN) where any origin of the dominant target photon field can be accommodated. For this purpose we reconstruct the minimum target photon spectrum required to produce the (observed) neutrino spectrum, and derive the distributions of all corresponding secondary particles. These initiate electromagnetic cascades with an efficiency that is linked to the neutrino production rate. The derived photon spectra represent the minimum radiation emerging from the source that is strictly associated with the photo-hadronically produced neutrinos. Using the 2014-15 neutrino spectrum observed by IceCube from TXS 0506+056, we conduct a comprehensive study of these cascade spectra and compare them to the simultaneous multi-wavelength emission. For this set of observations, photopion production from a co-spatially produced (co-moving) photon target can be ruled out as well as a setup where synchrotron or Compton-synchrotron supported cascades on a stationary (AGN rest frame) target photon field operate in this source. However, a scenario where Compton-driven cascades develop in the stationary soft-X-ray photon target which photo-hadronically produced the observed neutrinos appears feasible with required proton kinetic jet powers near the Eddington limit. The source is then found to produce neutrinos inefficiently, and emits GeV photons significantly below the observed Fermi-LAT-flux. Hence, the neutrinos and the bulk of the gamma rays observed in 2014/2015 from TXS 0506+056 cannot have been initiated by the same process.
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