Astroparticle Physics

7.5 Nature and Origin of the Highest-Energy Cosmic Rays 165The Markarian galaxies Mrk 421 and Mrk 501, whichhave been shown to be sources of photons of the highestenergies, would be candidates for the production of highenergyprotons. Since they are residing at distances of approximately100 Mpc, the arrival probability of protons fromthese distances with energies exceeding 10 20 eV, however, isonlyMarkarian galaxiesas cosmic-ray source?≈ e −x/λ ≈ 4 × 10 −5 . (7.25)Therefore protons can initiate the high-energy air-showerevents only if they come from relatively nearby sources (i.e.,from a local GZK sphere defined by distances < 30 Mpc,i.e., several mean free paths). The giant elliptical galaxyM87 lying in the heart of the Virgo cluster (distance ≈ 20Mpc) is one of the most remarkable objects in the sky. Itmeets all of the conditions for being an excellent candidatefor a high-energy cosmic-ray source.It is, however, possible to shift the effect of the Greisen–Zatsepin–Kuzmin cutoff to higher energies by assuming thatprimary particles are nuclei. Since the threshold energy mustbe available per nucleon, the corresponding threshold energy,for example, for carbon nuclei (Z = 6, A = 12) wouldbe correspondingly higher,M87 as particle accelerator?GZK sphereE = E p cutoff A = 7.2 × 1020 eV , (7.26)so that the observed events would not be in conflict with theGreisen–Zatsepin–Kuzmin cutoff. It is, however, difficult tounderstand, how atomic nuclei can be accelerated to suchhigh energies, without being disintegrated by photon interactionsor by fragmentation or spallation processes.One remote and rather drastic assumption to explain thetrans-GZK events would be a possible violation of Lorentzinvariance. If Lorentz transformations would not only dependon the relative velocity difference of inertial frames,but also on the absolute velocities, the threshold energy forγp collisions for interactions of blackbody photons withhigh-energy protons would be washed out and different fromγp collisions when photon and proton had comparable energies,thus evading the GZK cutoff.Photons as possible candidates for the observed highenergycascades are even more problematic. Because of theprocess of pair production of electrons and positrons offblackbody photons (see Sect. 6.3.3), photons have a relativelyshort mean free path ofheavy nucleiphoto disintegrationphotonsmean free path of photons