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.
