Time structure and multi-messenger signatures of ultra-high energy cosmic ray sources

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.