Abstract
The latest results on the sky distribution of ultra-high energy cosmic ray sources have consequences for their nature and time structure, if either deflection is moderate or if their density is comparable to or larger than the average density of active galaxies. If the sources accelerate predominantly nuclei of atomic number A and charge Z and emit continuously, their luminosity in cosmic rays above ≃6×1019 eV can be no more than a fraction of ≃5×10-4 Z-2 of their total power output. Such sources could produce a diffuse neutrino flux that gives rise to several events per year in neutrino telescopes of km3 size. Continuously emitting sources should be easily visible in photons below ∼100 GeV, but TeV γ-rays may be absorbed within the source. For episodic sources that accelerate cosmic rays in areas moving with a Lorentz factor Γ, the bursts or flares have to last at least ≃0.1 Γ-4 A-4 yr. A considerable fraction of the flare luminosity could then go into highest energy cosmic rays, in which case the rate of flares per source has to be less than ≃5×10- 3 Γ4 A4 Z2 yr-1. Episodic sources should typically have detectable variability both at FERMI/GLAST and TeV energies, but neutrino fluxes may be hard to detect. Finally, in contrast to γ-rays, power and density requirements make it unlikely that the ultra-high energy cosmic rays leave the source environment strongly beamed.
Highlights
5 × 10−4 Z −2 of their total power output
It has been shown that one-shot acceleration of UHECR with energy losses dominated by curvature radiation is possible [12, 28]. These mechanisms are consistent with the estimates discussed above and can potentially lead to UHECR production in flares
Where CR accounts for possible UHECR beaming. This is consistent with a recent Monte Carlo study of the auto-correlation function of the 27 UHECR events detected by the Pierre Auger experiment [29] above 57 EeV, which deduces a best fit range of ns = (4–14) × 10−5 Mpc−3 [32]
Summary
Accelerating particles of charge eZ to an energy Emax requires an induction E Emax/(eZ ). Any source producing UHECR up to energy Emax at a given time has to have a total power output of at least the Poynting luminosity equation (1). Note that this is comparable to the Eddington luminosity LEdd(M) = 1.3 × 1038(M/M ) erg s−1 of a massive black hole of mass M in the centers of active galaxies. There are some scenarios for acceleration close to the central supermassive black hole: this can occur, for example, due to the electromotive force induced by magnetic field threading the event horizon where the emitted power is driven by spin-down [25] and the accretion rate could be very small, giving rise to a ‘dead quasar’ [26]. These mechanisms are consistent with the estimates discussed above and can potentially lead to UHECR production in flares
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