Ultra-High Energy Cosmic Rays:
Propagation and Average Nucleon and Gamma Ray Fluxes

To this end, Sangjin Lee, whom I helped to turn this project into a PhD thesis under his advisor David Schramm (U of C), Paolo Coppi (Yale University), and myself developed an extensive numerical code for the propagation of extragalactic nucleons, gamma rays and electrons with energies between 100MeV and 10**(25) eV. As a result, we show that for large scale magnetic fields smaller than about 10**(-9) G, top down mechanisms spatially uniformly injecting gamma rays and nucleons up to 10**(16) GeV are still a viable explanation of the events observed above 10**(20) eV. This is in contrast to a recent claim that top down mechanisms might be ruled out altogether, either because the continuous energy injection throughout the history of the universe predicted in these models would overproduce the measured gamma ray background around 1GeV, or because after normalizing to the highest energy events, the integral flux at still higher energies would come out too high.

On the left is a representative result from our simulations which explicitly shows that the properly normalized predicted flux is consistent with all experimental data. It shows predictions for the differential fluxes of gamma rays (solid red line) and nucleons (dotted black line) by a top down model with a maximal injection energy of 10**(16) GeV, a typical Grand Unification scale, assuming supermassive particle decay into two quarks which produce about 10% nucleons and 90% pions with a spectrum motivated by supersymmetry. A vanishing extragalactic magnetic field was assumed, and some new relatively high theoretical estimates for the universal radio background (which is very uncertain but the dominant target for photon absorption around 100 EeV) were used. Also shown are the combined data from the Haverah Park, the Fly's Eye and the AGASA experiments above 10**(19) eV (data with error bars) and piecewise power law fits to the observed charged CR flux (thick solid line). Note that this model seems to explain all cosmic rays above 50 EeV and predicts the dip at 100 EeV to be associated with a cross over from a nucleon component to an about equal mixture of gamma rays and neutrinos. Experimental constraints on the diffuse gamma ray flux between 30 MeV and 100 GeV from the EGRET instrument onboard the Compton Gamma Ray Observatory (CGRO) are shown as the dash-dotted line on the left margin. Points with arrows represent upper limits on the diffuse gamma ray flux from the HEGRA, the Utah-Michigan, the EAS-TOP, and the CASA-MIA experiments, as indicated.

Furthermore, the numerical simulations suggest that ultra-high energy cosmic and gamma rays can also be used to detect and possibly measure an extragalactic magnetic field whose nature is still unknown. The discovery of a primordial field on scales larger than galaxy clusters is in principle possible with this method and could open a new window into processes occurring in the early universe. For example, together with Angela Olinto (U of C) we showed in this paper that, independent of the source nature, the cross-over between the electron energy ranges dominated by synchrotron and inverse Compton losses, respectively, leads to a feature in the ultra-high energy gamma ray spectrum which can be used to estimate the typical extragalactic magnetic field strength. We also realized that an average fraction of about 10% gamma rays in the total cosmic ray flux around 10**(19) eV would imply both a non-acceleration origin of the events above 10**(20) eV and a large scale extragalactic magnetic field weaker than about 10**(-11) G (see paper).

Ultra-high energy cosmic and gamma rays can be accompanied by sizeable ultra-high energy neutrino fluxes.

See also time-dependent ultra-high energy cosmic ray fluxes and cosmic magnetic fields.

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