Long-duration gamma-ray bursts (GRBs) have been often considered as the natural evolution of some core-collapse supernovae (SNe). While GRBs with relativistic jets emit an electromagnetic signal, GRBs with mildly relativistic jets are opaque to photons and therefore could be detectable through neutrinos only. We discuss the possibility that successful GRBs and mildly relativistic jets belong to the same class of astrophysical transients with different Lorentz factor ${\mathrm{\Gamma }}_b$ and study the production of high-energy neutrinos as a function of ${\mathrm{\Gamma }}_b$, by including both proton-photon and proton-proton interactions. By assuming a SN-GRB connection, we find that the diffuse neutrino emission from optically thick jets with Lorentz factors lower than the ones of successful GRBs can be one of the main components of the observed IceCube high-energy neutrino flux. Moreover, under the assumption that all these jets belong to the same class of astrophysical transients, we show that the IceCube high-energy neutrino data provide indirect constraints on the rate of nonsuccessful jets, favoring a local rate lower than tens of percent of the local SN rate. These limits are currently comparable to dedicated searches on choked sources and are expected to become tighter with the accumulation of more high-energy neutrino data.

• Received 9 December 2015

DOI:https://doi.org/10.1103/PhysRevD.93.053010