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Implications of gamma-ray observations on proton models of UHECR

The origin of ultra high energy cosmic rays (UHECR) is still unknown. However, great progress has been achieved in past years due to the good quality and large statistics in experimental data collected by the current observatories. The data of the Pierre Auger Observatory show that the composition of the UHECRs becomes progressively lighter starting from $10^{17}$ eV up to $\sim 10^{18.3}$ eV and then, beyond that energy, it becomes increasingly heavier. These analyses are subject to important systematic uncertainties due to the use of hadronic interaction models that extrapolate lower energy accelerator data to the highest energies. Although proton models of UHECRs are disfavored by these results, they cannot be completely ruled out. It is well known that the energy spectra of gamma rays and neutrinos, produced during propagation of these very energetic particles through the intergalactic medium, are a useful tool to constrain the spectrum models. In particular, it has recently been shown that the neutrino upper limits obtained by IceCube challenge the proton models at 95% CL. In this work we study the constraints imposed by the extragalactic gamma-ray background, measured by Fermi-LAT, on proton models of UHECRs. In particular, we make use of the extragalactic gamma-ray background flux, integrated from 50 GeV to 2 TeV, that originates in point sources, which has recently been obtained by the Fermi-LAT collaboration, in combination with the neutrino upper limits, to constrain the emission of UHECRs at high redshits ($z>1$), in the context of the proton models.