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There are two promising scenarios that explain the ankle, which is a dip inthe spectrum of cosmic rays at $\sim 10^{19}$ eV. A scenario interprets theankle as the transition from Galactic to extragalactic cosmic rays ({\itankle-transition scenario}), while the other is that the dip caused by pairproduction on the cosmic microwave background radiation ({\it proton-dipscenario}). In this paper, we consider whether cosmogenic neutrinos can be aclue to judge which scenario is favored. We calculated the fluxes of cosmogenicneutrinos following these scenarios with plausible physical parameter sets, andfound several important features as follows. First of all, the neutrino flux at$\sim 10^{20}$ eV becomes much higher in the ankle-transition scenario as longas the maximum energy of the cosmic rays at sources is sufficiently high. Onthe other hand, the neutrino spectrum has a characteristic peak at $\sim10^{16}$ eV in the proton-dip scenario on the condition that extragalacticprotons significantly contribute to the observed cosmic rays down to $10^{17}$eV. Thus, we conclude cosmogenic neutrinos should give us a clue to judge whichscenario is favored, unless these features are masked by the neutrinobackground coming from possible, powerful neutrino sources such as AGNs andGRBs. We also found an interesting feature that the neutrino flux at $\sim10^{18}$ eV depends only on the cosmological evolution of the cosmic raysources. That means cosmogenic neutrinos with the energy bring us informationon the cosmological evolution of the sources of ultra-high energy cosmic rays.Finally, we compare the fluxes of cosmogenic neutrinos with the expectedsensitivity curves of several neutrino detectors, and conclude the detection ofcosmogenic neutrinos in the near future is promising.

Cosmogenic neutrinos as a probe of the transition from Galactic to extragalactic cosmic rays