The origin of the bulk of the high-energy astrophysical neutrinos seen by IceCube, with TeV--PeV energies, is unknown. If they are made in photohadronic, i.e., proton-photon, interactions in astrophysical sources, this may manifest as a bump-like feature in their diffuse flux, centered around a characteristic energy. We search for evidence of this feature, allowing for variety in its shape and size, in 7.5 years of High-Energy Starting Events (HESE) collected by the IceCube neutrino telescope, and make forecasts using larger data samples from upcoming neutrino telescopes. Present-day data reveals no evidence of bump-like features, which allows us to constrain candidate populations of photohadronic neutrino sources. Near-future forecasts show promising potential for stringent constraints or decisive discovery of bump-like features. Our results provide new insight into the origins of high-energy astrophysical neutrinos, complementing those from point-source searches.
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