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tokens: cool via synchrotron and IC losses. Following Murase ( 2012 ), the deflection angle during the radiation cooling time is given bywhere t syn is the synchrotron cooling time, r L is the Larmor radius, and the Lorentz factor of pairs in the black hole rest frame is . Only synchrotron cooling is considered, because the IC cooling is suppressed for such high-energy electrons and positrons. The above equation implies that the pairs lose their energy after they become isotropized. Note that the X-ray emission is doubly suppressed, because the deflection is larger than the jet opening angle, i.e., , and the time spread in the cascade emission is longer than the intrinsic flare duration, i.e., . Also, the CR neutrons do not produce extra pairs via the Bethe–Heitler process. In addition, in the np scenario, X-rays could also be isotropized via the Compton scattering. Thus, X-rays from the neutral beam can be highly suppressed if the CR energy is lower than UHE energies, and the associated hadronic cascade signatures can be masked by the GeV γ -ray emission from the blazar zone. Note that the UHE neutron beam, if it exists, can also produce beamed cascade emission at TeV energies. The resulting synchrotron pair-echo emission (Dermer et al. 2012 ; Murase 2012 ) is expected to have some time delay. We also remark that the very high energy flare seen by MAGIC was detected about 10 days later after IceCube-170922A. 4. Summary We considered implications of the high-energy neutrino flares from TXS 0506+056 by examining various constraints. Flaring blazars could be the brightest sources in the neutrino sky, while the observations can most naturally be reconciled with existing theoretical models, if the blazars are subdominant (∼1%–10%) in the diffuse neutrino intensity. Interestingly, within the standard leptonic scenario of γ -ray emission, we found that the blazar neutrino emission itself can readily be dominated by flaring episodes. This could explain why the significant neutrino signals from TXS 0506+056 were found only in the time-dependent search and that the steady component that typically dominates γ -ray emission has not been seen yet in neutrinos. Bright neutrino flares like the ones observed for TXS 0506+056 could contribute only up to a few percent of the INB. If the association with this blazar is physical, such flares can be detected with a rate of by dedicated time-dependent searches in the near future. Based on analytical considerations, we also showed the importance of X-ray constraints to test the physical models of TXS 0506+056. An efficient electromagnetic cascade is unavoidable in the canonical blazar models based on the single radiation zone, which also predicts that the 2014–2015 neutrino flare found in the archival data should be accompanied by X-ray emission with . This can readily be tested by X-ray sky monitors such as Swift and MAXI . Nondetection of the X-ray flares will necessitate more complicated models involving multizone