Aims. We consider particle acceleration in vacuum gaps in magnetospheres of black holes powered through Blandford-Znajek mechanism and embedded into radiatively-inefficient accretion flow (RIAF) environment. In such situation the gap height is limited by the onset of gamma-gamma pair production on the infrared photons originating from the RIAF. Methods. We numerically calculate acceleration and propagation of charged particles taking into account the detailed structure of electric and magnetic field in the gap and in the entire black hole magnetosphere, radiative energy losses and interactions of γ-rays produced by the propagated charged particles with the background radiation field of RIAF.Results. We show that the presence of the vacuum gap has clear observational signatures. The spectra of emission from gaps embedded into a relatively high luminosity RIAF are dominated by the inverse Compton emission with a sharp, super-exponential cut-off in the very-high-energy gamma-ray band. The cut-off energy is determined by the properties of the RIAF and is largely independent of the structure of magnetosphere and geometry of the gap. The spectra of the gap residing in low-luminosity RIAFs are dominated by synchrotron / curvature emission with the spectra extending into 1-100 GeV energy range. We also consider the effect of possible acceleration of protons in the gap and find that proton energies could reach the ultra-high-energy cosmic ray (UHECR) range only in extremely low luminosity RIAFs.
We review basic constraints on the acceleration of ultra-high-energy (UHE) cosmic rays (CRs) in astrophysical sources, namely the geometrical (Hillas) criterion and restrictions from radiation losses in different acceleration regimes. Using the latest available astrophysical data, we redraw the Hillas plot and figure out potential UHECR accelerators. For the acceleration in central engines of active galactic nuclei, we constrain the maximal UHECR energy for a given black-hole mass. Among active galaxies, only the most powerful ones, radio galaxies and blazars, are able to accelerate protons to UHE, though acceleration of heavier nuclei is possible in much more abundant lowerpower Seyfert galaxies.
Context. 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 γ-ray emission is accompanied by neutrino emission with comparable energy flux but with a different spectrum. Aims. We derive constraints on the hadronic models of activity of blazars imposed by non-detection of neutrino flux from a population of γ-ray emitting blazars. Methods. We stack the γ-ray and muon neutrino flux from 749 blazars situated in the declination strip above −5 • . Results. 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 10 19 eV.1
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