Modelling the coincident observation of a high-energy neutrino and a bright blazar flare

In September 2017, the IceCube Neutrino Observatory recorded a very-high-energy neutrino in directional coincidence with a blazar in an unusually bright gamma-ray state, TXS0506？+？056 (refs1,2). Blazars are prominent photon sources in the Universe because they harbour a relativistic jet whose radiation is strongly collimated and amplified. High-energy atomic nuclei known as cosmic rays can produce neutrinos; thus, the recent detection may help in identifying the sources of the diffuse neutrino flux3 and the energetic cosmic rays. Here we report a self-consistent analysis of the physical relation between the observed neutrino and the blazar, in particular the time evolution and spectral behaviour of neutrino and photon emission. We demonstrate that a moderate enhancement in the number of cosmic rays during the flare can yield a very strong increase in the neutrino flux, which is limited by co-produced hard X-rays and teraelectronvolt gamma rays. We also test typical radiation models4,5 for compatibility and identify several model classes6,7 as incompatible with the observations. We investigate to what degree the findings can be generalized to the entire population of blazars, determine the relation between their output in photons, neutrinos and cosmic rays, and suggest how to optimize the strategy of future observations