High energy neutrino emission and neutrino background from gamma-ray bursts in the internal shock model

High energy neutrino emission from gamma-ray bursts (GRBs) is discussed. In this paper, by using the simulation kit GEANT4, we calculate proton cooling efficiency including pion-multiplicity and proton-inelasticity in photomeson production. First, we estimate the maximum energy of accelerated protons in GRBs. Using the obtained results, neutrino flux from one burst and a diffuse neutrino background are evaluated quantitatively. We also take account of cooling processes of pion and muon, which are crucial for resulting neutrino spectra. We confirm the validity of analytic approximate treatments on GRB fiducial parameter sets, but also find that the effects of multiplicity and high-inelasticity can be important on both proton cooling and resulting spectra in some cases. Finally, assuming that the GRB rate traces the star formation rate, we obtain a diffuse neutrino background spectrum from GRBs for specific parameter sets. We introduce the nonthermal baryon-loading factor, rather than assume that GRBs are main sources of ultra-high energy cosmic rays (UHECRs). We find that the obtained neutrino background can be comparable with the prediction of Waxman and Bahcall, although our ground in estimation is different from theirs. In this paper, we study on various parameters since there are many parameters in the model. The detection of high energy neutrinos from GRBs will be one of the strong evidences that protons are accelerated to very high energy in GRBs. Furthermore, the observations of a neutrino background has a possibility not only to test the internal shock model of GRBs but also to give us information about parameters in the model and whether GRBs are sources of UHECRs or not.