On the Neutrino Flares from the Direction of TXS 0506+056

A multimessenger campaign has associated a high-energy cosmic neutrino with a distant gamma-ray blazar, TXS 0506+056. IceCube archival data subsequently revealed that the high-energy neutrino flux from the direction of this source, integrated over the last 10 yr, is dominated by a single bright neutrino flare in 2014, leaving the multimessenger flare as a subluminous second flare. The extraordinary brightness of the blazar despite its distance suggests that it may belong to a special class of sources that produce cosmic rays. We show that the diffuse IceCube flux discovered in 2013 can be accommodated by a subclass of blazars, on the order of 5%, that episodically produce neutrinos with the luminosity of the 2014 neutrino flare. Matching the cosmic-ray flux required to produce the neutrinos to the one observed implies highly efficient neutrino sources with large target photon densities that are not transparent to high-energy gamma-rays. The opacity of the source modifies the straightforward multimessenger connection in a way that is consistent with the gamma-ray observations coincident with the 2014 neutrino flare.