GRB neutrino spectra (the prompt spectrum emitted by the sources and neutrino spectrum generated in GZK interactions are shown separately), assuming the luminosity range and star-forming redshift evolution of the sources. Here, are the fractional energies in the fireball carried by the electrons and the magnetic field; the two are equal in the case of equipartition. is the photon energy in units of erg. We show the prompt spectra separately for models where the fireball's dynamical time scale is smaller (larger) than the synchrotron loss time scale (green right-hatched and blue cross-hatched, resp.). Here, the dynamical time scale is just the variability scale and . The IceCube limits [46] on the total neutrino flux from the analysis of high-energy and ultra-high-energy muon neutrinos with the 40-string subarray assume 1 : 1 : 1 flavor composition after oscillation. We also show the sensitivity of the full IceCube detector (IC-86) to muon neutrinos after 3 years of observation. The gray solid area shows the range of GZK neutrinos expected at the 99% C.L.
