Signatures of the transition from galactic to extragalactic cosmic rays

We discuss the signatures of the transition from galactic to extragalactic cosmic rays in different scenarios, giving the most attention to the dip scenario. The dip is a feature in the diffuse spectrum of ultrahigh-energy protons in the energy range $1\times {10}^{18}–4\times {10}^{19}\mathrm{eV}$, which is caused by electron-positron pair production on the cosmic microwave background radiation. The dip scenario provides a simple physical description of the transition from galactic to extragalactic cosmic rays. Here we summarize the signatures of the pair-production dip model for the transition, most notably the spectrum, the anisotropy, and the chemical composition. The main focus of our work is, however, on the description of the features that arise in the elongation rate and in the distribution of the depths of shower maximum $X_{\max }$ in the dip scenario. We find that the curve for $X_{\max }(E)$ shows a sharp increase with energy, which reflects a sharp transition from an iron-dominated flux at low energies to a proton-dominated flux at $E\sim {10}^{18}\mathrm{eV}$. We also discuss in detail the shape of the $X_{\max }$ distributions for cosmic rays of given energy and demonstrate that this represents a powerful tool to discriminate between the dip scenario and other possible models of the transition.