Cosmic-Ray and Neutrino Emission from Gamma-Ray Bursts with a Nuclear Cascade

We discuss neutrino and cosmic-ray emission from Gamma-Ray Bursts (GRBs) with the injection of nuclei, where we take into account that a nuclear cascade from photo-disintegration can fully develop in the source. One of our main objectives is to test if recent results from the IceCube and the Pierre Auger Observatory can be accommodated with the paradigm that GRBs are the sources of Ultra-High Energy Cosmic Rays (UHECRs). While our key results are obtained using an internal shock model, we discuss how the secondary emission from a GRB shell can be interpreted in terms of other astrophysical models. It is demonstrated that the expected neutrino flux from GRBs weakly depends on the injection composition, which implies that prompt neutrinos from GRBs can efficiently test the GRB-UHECR paradigm even if the UHECRs are nuclei. We show that the UHECR spectrum and composition, as measured by the Pierre Auger Observatory, can be self-consistently reproduced in a combined source-propagation model. In an attempt to describe the energy range including the ankle, we find tension with the IceCube bounds from the GRB stacking analyses. In an alternative scenario, where only the UHECRs beyond the ankle originate from GRBs, the requirement for a joint description of cosmic-ray and neutrino observations favors lower luminosities, which does not correspond to the typical expectation from $\gamma$-ray observations