Signatures of the extragalactic cosmic-ray source composition from spectrum and shower depth measurements

We discuss the differences induced by the assumed composition of extragalactic sources on the predicted UHECR spectrum and the energy evolution of $<X_{\max}>$, i.e. the mean value of the atmospheric depth at the cosmic-ray air shower maximum. We show that different assumptions for the source power evolution do not modify our earlier finding that in the case of a mixed composition the ankle can be interpreted as the end of the transition from galactic to extragalactic cosmic rays. We show the characteristic features in the shape of $<X_{\max}>$(E) that are associated with this transition for each cosmic-ray composition model. These characteristic features are present whatever the hadronic model used for the calculation. In the mixed composition cases, a signature of the interactions of nuclei with the photon backgrounds is also expected above $10^{19}$ eV. The comparisons with Stereo HiRes and Fly's Eye data favour an extragalactic mixed composition and the corresponding interpretation of the ankle. Confrontation of model predictions with future data at the highest energies will allow a better determination of the transition features and of the cosmic-ray source composition, independently of hadronic models. We also emphasize that in the pure proton case, a combined analysis of the spectrum and composition below the ankle could lead to constraints on the source power evolution with redshift.