Indications of Negative Evolution for the Sources of the Highest Energy Cosmic Rays

Using recent measurements of the spectrum and chemical composition of the highest energy cosmic rays, we consider the sources of these particles. We find that the data strongly prefers models in which the sources of the ultra-high energy cosmic rays inject predominantly intermediate mass nuclei, with comparatively few protons or heavy nuclei, such as iron or silicon. If the number density of sources per comoving volume does not evolve with redshift, the injected spectrum must be very hard ($\alpha \simeq 1$) in order to fit the spectrum observed at Earth. Such a hard spectral index would be surprising and difficult to accommodate theoretically. In contrast, much softer spectral indices, consistent with the predictions of Fermi acceleration ($\alpha\simeq 2$), are favored in models with negative source evolution. With this theoretical bias, these observations thus favor models in which the sources of the highest energy cosmic rays are preferentially located within the low-redshift universe.