Strong constraint on hadronic models of blazar activity from Fermi and IceCube stacking analysis

High-energy emission from blazars is produced by electrons which are either accelerated directly (the assumption of leptonic models of blazar activity) or produced in interactions of accelerated protons with matter and radiation fields (the assumption of hadronic models). The hadronic models predict that gamma-ray emission is accompanied by neutrino emission with comparable energy flux but with a different spectrum. We derive constraints on the hadronic models of activity of blazars imposed by non-detection of neutrino flux from a population of gamma-ray emitting blazars. We stack the gamma-ray and muon neutrino flux from 749 blazars situated in the declination strip above -5 degrees. Non-detection of neutrino flux from the stacked blazar sample rules out the proton induced cacade models in which the high-energy emission is powered by interactions of shock-accelerated proton beam in the AGN jet with the ambient matter or with the radiation field of the black hole accretion disk. The result remains valid also for the case of interactions in the scattered radiation field in the broad line region. IceCube constraint could be avoided if the spectrum of accelerated protons is sharply peaking in the ultra-high-energy cosmic ray range, as in the models of acceleration in the magnetic reconnection regions or in the vacuum gaps of black hole magnetospheres. Models based on these acceleration mechanisms are consistent with the data only if characteristic energies of accelerated protons are higher than 1e19 eV.