Gamma-ray bursts (GRBs) are one of the candidates of ultrahigh-energy ($\gtrsim {10}^{18.5}\mathrm{eV}$) cosmic-ray (UHECR) sources. We investigate high-energy cosmic-ray acceleration including heavy nuclei in GRBs by using Geant 4, and discuss its various implications, taking both high-luminosity (HL) and low-luminosity (LL) GRBs into account. This is because LL GRBs may also make a significant contribution to the observed UHECR flux if they form a distinct population. We show that not only protons, but also heavier nuclei can be accelerated up to ultrahigh energies in the internal, (external) reverse, and forward shock models. We also show that the condition for ultrahigh-energy heavy nuclei such as iron to survive is almost the same as that for $\sim \mathrm{TeV}$ gamma rays to escape from the source and for high-energy neutrinos not to be much produced. The multimessenger astronomy by neutrino and GeV-TeV gamma-ray telescopes such as IceCube and KM3Net, GLAST and MAGIC will be important to see whether GRBs can be accelerators of ultrahigh-energy heavy nuclei. We also demonstrate expected spectra of high-energy neutrinos and gamma rays, and discuss their detectabilities. In addition, we discuss implications of the GRB-UHECR hypothesis. We point out, since the number densities of HL GRBs and LL GRBs are quite different, its determination by UHECR observations is also important.

• Received 18 January 2008

DOI:https://doi.org/10.1103/PhysRevD.78.023005