On the neutrino non-detection of GRB 130427A

The recent gamma-ray burst GRB 130427A has an isotropic electromagnetic energy E ^iso ∼ 10⁵⁴ erg, suggesting an ample supply of target photons for photo-hadronic interactions, which at its low redshift of z ∼ 0.34 would appear to make it a promising candidate for neutrino detection. However, the IceCube collaboration has reported a null result based on a search during the prompt emission phase. We show that this neutrino non-detection can provide valuable information about this gamma-ray burst's (GRB's) key physical parameters such as the emission radius R_d , the bulk Lorentz factor Γ, and the energy fraction converted into cosmic rays εp. The results are discussed both in a model-independent way and in the specific scenarios of an internal shock (IS) model, a baryonic photospheric (BPH) model, and a magnetic photospheric (MPH) model. We find that the constraints are most stringent for the MPH model considered, but the constraints on the IS and the BPH models are fairly modest.