UHECRs are the highest energy particles arriving at earth. While propagating in the intergalactic medium (IGM) charged UHECRs are deflected by intergalactic magnetic fields and interact with radiation fields through essentially photo-pion production reactions and photodisintegration of nuclei. Such interactions have typical mean-free paths on the order of tenth or hundreds of Mega-parsec, and the energy lost in one interaction is typically of the order of a few percent or up to 20% of the initial particle energy in case of nucleons. The energy loss for nuclei in photo disintegration reactions can be even larger, up to 67%. Additionally, primary nuclei can lose nucleons in these interactions thereby changing their type. Given the accuracy of present day experiments, like the Pierre Auger Observatory (PAO), the propagation of charged UHECRs must then be described within a Monte Carlo approach.
The main observational properties of UHECRs are their energy spectrum, their mass composition and their arrival directions, which in turn are determined by various physical properties of the IGM and of the UHECR sources, which we list below:
- The source properties and distribution. The sources of charged UHECRs are currently unknown, but may be active galactic nuclei (AGNs) or gamma ray bursts (GRBs). Independent of their true nature, the most important ingredient is their injection spectra and their distribution in the local universe. In particular, the ``end of the spectrum of UHECRs might be dominated by nearby sources. The spectrum and anisotropies at these energies depend on the exact source configuration.
- The interactions with low-energy backgrounds. Charged nuclei undergo pair and pion production, and therefore generate secondary neutrinos and electromagnetic cascades whose detection might provide important hints to the sources of UHECRs, as has already been the case at lower energy. Additionally nuclei photodisintegrate on low energy backgrounds. Subsequently unstable nuclei produced in the aforementioned interactions decay.
- The deflections in magnetic fields. Although they are very poorly known, magnetic fields might play a significant role even for the highest energy particles, by deflecting their propagation direction and increasing the mean path from the source to the observer.
- The composition of the injected cosmic rays. The composition of UHECRs at injection influences the reactions of cosmic rays in low energy photon backgrounds as well as the deflections of their trajectories.