The IceCube Collaboration recently reported a stringent upper limit on the high energy neutrino flux from gamma-ray bursts (GRBs), which provides a meaningful constraint on the standard internal shock model. Recent broadband electromagnetic observations of GRBs also challenge the internal shock paradigm for GRBs, and some competing models for $\gamma$-ray prompt emission have been proposed. We describe a general scheme for calculating the GRB neutrino flux, and compare the predicted neutrino flux levels for different models. We point out that the current neutrino flux upper limit starts to constrain the standard internal shock model. The dissipative photosphere models are also challenged if the cosmic ray luminosity from GRBs is at least 10 times larger than the $\gamma$-ray luminosity. If the neutrino flux upper limit continues to go down in the next few years, then it would suggest the following possibilities: (i) the photon-to-proton luminosity ratio in GRBs is anomalously high for shocks, which may be achieved in some dissipative photosphere models and magnetic dissipation models; or (ii) the GRB emission site is at a larger radius than the internal shock radius, as expected in some magnetic dissipation models such as the internal collision-induced magnetic reconnection and turbulence model.

• Received 2 October 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.121101