We explore the joint implications of ultrahigh energy cosmic ray (UHECR) source environments -- constrained by the spectrum and composition of UHECRs -- and the observed high energy astrophysical neutrino spectrum. Acceleration mechanisms producing power-law CR spectra $propto E^{-2}$ are compatible with UHECR data, if CRs at high rigidities are in the quasi-ballistic diffusion regime as they escape their source environment. Both gas- and photon-dominated source environments are able to account for UHECR observations, however photon-dominated sources do so with a higher degree of accuracy. However, gas-dominated sources are in tension with current neutrino constraints. Accurate measurement of the neutrino flux at $sim 10$ PeV will provide crucial information on the viability of gas-dominated sources, as well as whether diffusive shock acceleration is consistent with UHECR observations. We also show that UHECR sources are able to give a good fit to the high energy portion of the astrophysical neutrino spectrum, above $sim$ PeV. This common origin of UHECRs and high energy astrophysical neutrinos is natural if air shower data is interpreted with the textsc{Sibyll2.3c} hadronic interaction model, which gives the best-fit to UHECRs and astrophysical neutrinos in the same part of parameter space, but not for EPOS-LHC.
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