Neutrino spectra from low and high luminosity populations of gamma ray bursts

The detection of GRB 060218 at z=0.033z=0.033 by Swift   within 1.5 years of operation, together with the detection of GRB 980425 at z=0.0085z=0.0085 by BeppoSAX, suggest that these low luminosity (LL) GRBs have a much higher event rate than the canonical high luminosity (HL) GRBs, and they form a distinct new component in the GRB luminosity function. We explore the contribution of this previously neglected GRB population to the diffuse neutrino background within the internal shock model and compare it with that of the canonical HL population. By considering a wide range of distributions of various parameters (e.g. luminosity, spectral break energy, duration, variability time, Lorentz factor, redshift) for both populations, we find that although it is difficult to detect neutrinos from the individual LL GRBs, the contribution of the LL population to the diffuse neutrino background is more than the HL population above about 108 GeV.