Can Experiments Studying Ultrahigh Energy Cosmic Rays Measure the Evolution of the Sources?

Interactions between cosmic ray protons and the photons of the cosmic microwave background radiation, as well as the expansion of the universe, cause cosmic rays to lose energy in a way that depends on the distance from the cosmic nray source to the earth. Because of this, there is a correlation between cosmic ray energies and the average redshift of their origin. This correlation may be exploited to measure the evolution of the sources of cosmic rays. Sky surveys of Quasi Stellar Objects (QSO's) and Active Galactic Nuclei (AGN's), made at optical and x-ray wavelengths, are consistent in showing that the evolution of such objects exhibits a break at a redshift, z, of about 1.6. At smaller redshifts, the luminosity density of QSO's and AGN's follows a $(1+z)^m$ distribution, with $m \sim 2.6$, and exhibit a much flatter distribution above the break. Measurements of the star formation rate are also consistent with this picture. If QSO's and AGN's are sources of ultrahigh energy cosmic rays the break in their evolution should appear in the cosmic ray spectrum at an energy of about $10^{17.6}$ eV. This is the energy of the second knee.