A scenario for the Galactic cosmic rays between the knee and the second-knee

We perform a fit to measurements of the cosmic ray spectrum and of the depth of shower maximum in the energy range between $10^{15}$~eV and $10^{18}$~eV. We consider a Galactic component that is a mixture of five representative nuclear species (H, He, N, Si and Fe), for which we adopt rigidity dependent broken power-law spectra, and we allow for an extragalactic component which becomes strongly suppressed for decreasing energies. The relative abundances of the Galactic components at $10^{15}$~eV are taken to be comparable to those determined by direct measurements at $10^{13}$~eV. The main features of the spectrum and of the composition are reproduced in these scenarios. The spectral knee results from the break of the H spectrum at $E_{\rm k}\simeq 3\times 10^{15}$~eV, although it is broaden by the comparable contribution from He which has a break at about $6\times 10^{15}$~eV. The low-energy ankle at $E_{\rm la}\simeq 2\times 10^{16}$~eV is associated to the strong suppression of the H and He Galactic components and the increasing relative contribution of the heavier ones, but the observed hardening of the spectrum at this energy turns out to result from the growing contribution of the extragalactic component. The second-knee at $E_{\rm sk}\simeq 26 E_{\rm k}\simeq 8\times 10^{16}$~eV is associated with the steepening of the Galactic Fe component. The transition to the regime in which the total cosmic ray flux is dominated by the extragalactic component takes place at an energy of about $10^{17}$~eV. The parameters of the fit depend on the hadronic model that is used to interpret the $X_{\rm max}$ measurements as well as on the specific $X_{\rm max}$ dataset that is considered in the fit. The impact of the possible existence of a maximum rigidity cutoff in the Galactic components is also discussed.