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Self-consistent neutrino and UHE cosmic ray spectra from Mrk 421

We examine the neutrino and cosmic ray spectra resulting from two models of fitting the spectral energy distribution (SED) of the blazar Mrk~421 using a self-consistent leptohadronic code. The $γ$-ray emission is attributed to either synchrotron radiation of ultra-high energy protons (LHs model) or to synchrotron radiation from electrons that result from photopion interactions of lower energy protons (LH$π$ model). Although both models succeed in fitting satisfactorily the SED, the parameter values that they use result in significantly different neutrino and cosmic-ray spectra. For the LH$π$ model, which requires high proton energy density, we find that the neutrino spectrum peaks at an energy $E_{\rm ν,peak}= 3.3$ PeV which falls well within the energy range of recent neutrino observations. While at the same time its peak flux is just under the sensitivity limit of IC-40 observations, it cannot produce ultra-high energy cosmic rays. In the LHs model, on the other hand, neutrinos are far from being detectable because of their low flux and peak energy at $E_{\rm ν,peak} \simeq 100$ PeV. However, the propagation of protons produced by the decay of escaping neutrons results in an ultra-high energy cosmic ray flux close to that observed by Pierre Augere, HiRes and Telescope Array at energies $E_p \simeq 30$ EeV.