Ultra high energy cosmic rays from non-relativistic quasar outflows

It has been suggested that non-relativistic outflows from quasars can naturally account for the missing component of the extragalactic $\gamma$-ray background and explain the cumulative neutrino background through pion decay in collisions between protons accelerated by the outflow shock and interstellar protons. Here we show that the same quasar outflows are capable of accelerating protons to energies of $\sim 10^{20}$ eV during the early phase of their propagation. The overall quasar population is expected to produce a cumulative ultra high energy cosmic ray flux of $\sim10^{-7}\,\rm GeV\,cm^{-2}s^{-1}sr^{-1}$ at $E_{\rm CR}\gtrsim10^{18}$ eV. The spectral shape and amplitude is consistent with recent observations for outflow parameters constrained to fit secondary $\gamma$-rays and neutrinos without any additional parameter tuning. This indicates that quasar outflows simultaneously account for all three messengers at their observed levels.