The origin of the TeV--PeV astrophysical neutrinos seen by the IceCube
telescope is unknown. If they are made in proton-photon interactions in
astrophysical sources, their spectrum may show bump-like features. We search
for such features in the 7.5-years High-Energy Starting Events (HESE), and
forecast the power of such searches using larger data samples expected from
upcoming 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.Comment: Submitted as a proceeding for ICRC 2023. arXiv admin note:
substantial text overlap with arXiv:2301.0002