Neutrino diagnostics of ultra-high energy cosmic ray protons

The energy at which cosmic rays from extra-galactic sources begin to dominate over those from galactic sources is an important open question in astroparticle physics. A natural candidate is the energy at the 'ankle' in the approximately power-law energy spectrum which is indicative of a cross-over from a falling galactic component to a flatter extra-galactic component. The transition can occur without such flattening but this requires some degree of conspiracy of the spectral shapes and normalizations of the two components. Nevertheless it has been argued that extra-galactic sources of cosmic ray protons which undergo interactions on the CMB can reproduce the energy spectrum below the ankle if the cross-over energy is as low as the 'second knee' in the spectrum. This low cross-over model is constrained by direct measurements by the Pierre Auger Observatory which indicate a heavier composition at these energies. We demonstrate that upper limits on the cosmic diffuse neutrino flux provide a complementary constraint on the proton fraction in ultra-high energy extra-galactic cosmic rays and forthcoming data from IceCube will provide a definitive test of this model.