Magnetized Sources of Ultra-high Energy Nuclei and Extragalactic Origin of the Ankle

It has recently been suggested that ultra-high energy cosmic rays could have an extragalactic origin down to the "second knee" at ~4x10^{17}eV. In this case the "ankle" or "dip" at ~5x10^{18}eV would be due to pair production of extragalactic protons on the cosmic microwave background which requires an injection spectrum of about E^{-2.6}. It has been pointed out that for injection of a mixed composition of nuclei a harder injection spectrum \~E^{-2.2} is required to fit the spectra at the highest energies and a galactic component is required in this case to fit the spectrum below the ankle, unless the proton fraction is larger than 85%. Here we perform numerical simulations and find that for sufficiently magnetized sources, observed spectra above 10^{19}eV approach again the case of pure proton injection due to increased path-lengths and more efficient photo-disintegration of nuclei around the sources. This decreases secondary fluxes at a given energy and thus requires injection spectra ~E^{-2.6}, as steep as for pure proton injection. In addition, the ankle may again be sufficiently dominated by protons to be interpreted as a pair production dip.
Comment: 12 latex pages, 9 ps figures included