IceCube has detected many TeV-PeV neutrinos, but their astrophysical origins remain largely unknown. Motivated by the observed late-Time X-ray/optical bumps in some gamma-ray bursts (GRBs), we examine the correlation between IceCube neutrinos and GRBs allowing delayed neutrinos ∼days after the prompt gamma-rays. Although we have not found any definitive correlation, up to ∼10% of the events observed so far at IceCube may have been neutrinos produced by the late-Time GRB activities at ∼1 day. Assuming a connection between some IceCube events and the late GRB bumps, we show in a model-independent way that GRB sites capable of producing late ∼PeV neutrinos should be nonrelativistic or mildly relativistic. We estimate the diffuse neutrino flux from such sources and find that they can possibly account for a few IceCube events. Future observations of high-energy neutrinos and late-Time GRB afterglows can further test the above proposed connection.
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