We revisit the neutrino and ultra high-energy cosmic ray ( UHECR ) production from gamma-ray bursts ( GRBs ) with time-dependent simulations for the proton-induced cascades .
This method can generate self-consistent photon , neutrino and escaped neutron spectra .
To obtain the integrated background spectra , we take into account the distributions of the burst luminosity and pulse duration timescale .
A benchmark case with standard GRB luminosity function , a bulk Lorentz factor \Gamma = 300 and a proton to gamma-ray luminosity fraction f _ { p } = 10 , is consistent with both the neutrino upper-limits and the observed UHECR intensity at \sim 10 ^ { 20 } eV , while requiring a different type of UHECR source at the ankle .
For the benchmark case the GRBs in the bright end of the luminosity function , which contribute most of the neutrinos , have their photon spectrum substantially distorted by secondary photons .
Such bright GRBs are few in number , and reducing their f _ { p } eliminates the distortion , while reducing the neutrino production .
Even if we neglect the contribution of the brightest GRBs , the UHECR production rate at GZK energies is almost unchanged .
These nominal GRB models , especially with L _ { iso } \lesssim 10 ^ { 53 } ~ { } \mbox { erg } ~ { } \mbox { s } ^ { -1 } , appear to meet the current constraints as far as being candidate UHECR sources above the ankle energy .