Density plot of expected neutrino event number in IceCube based on the internal shock model for GRB 130427A. The total number N _tot (muons + cascades) and N _μ (muons only) are calculated in the two-dimensional parameter space η and _p . Here, R _d is the internal shock radius for a 1 ms variability timescale (see Section 3). The value of N is represented the by color; however, for N _tot and N _μ the value of the color coding is different—see the upper and lower legends. The contours where N _tot = 1 and N _μ = 1 are also shown by solid and dashed lines, respectively. The other energy fractions are taken as constants, _e = 0.1 and _B = 0.01. The IceCube null result favors the yellow and blue regions, e.g., a high η.