Astroparticle Physics

5.7 Energy Spectra of Primary Particles 73The variable magnetic field of the neutron star whichis perpendicular to the accretion disk will produce via theLorentz force a strong electric field. Usingaccretion disksF = e(v × B) = eE , (5.28)the particle energy E is obtained, using v ⊥ B, to∫E = F · ds = evBs . (5.29)Under plausible assumptions (v ≈ c, B = 10 6 T, s =10 5 m) particle energies of 3 × 10 19 eV are possible. Even active galactic nucleimore powerful are accretion disks which form around blackholes or the compact nuclei of active galaxies. One assumesthat in these active galactic nuclei and in jets ejected fromsuch nuclei, particles can be accelerated to the highest energiesobserved in primary cosmic rays.The details of these acceleration processes are not yetfully understood. Sites in the vicinity of black holes – abillion times more massive than the Sun – could possiblyprovide the environment for the acceleration of the highestenergycosmic rays. Confined highly relativistic jets are acommon feature of such compact sources. It is assumed thatthe jets of particles accelerated near a black hole or the nucleusof a compact galaxy are injected into the radiation fieldof the source. Electrons and protons accelerated in the jetsvia shocks initiate electromagnetic and hadronic cascades. beamed jets from black holesHigh-energy γ rays are produced by inverse Compton scatteringoff accelerated electrons. High-energy neutrinos arecreated in the decays of charged pions in the development ofthe hadronic cascade. It is assumed that one detects emissionfrom these sources only if the jets are beamed into our lineof sight. A possible scenario for the acceleration of particlesin beamed jets from massive compact sources is sketched inFig. 5.8.5.7 Energy Spectra of Primary Particles“Get first your facts right and then youcan distort them as much as you please.”Mark TwainAt the present time it is not at all clear which of the presentedmechanisms contribute predominantly to the accelerationof cosmic-ray particles. There are good arguments to