Cosmic ray and neutrino emission from gamma-ray bursts with a nuclear cascade

Aims. 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 photodisintegration can fully develop in the source. Our main objective is to test whether recent results from the IceCube and the Pierre Auger Observatory can be accommodated within the paradigm that GRBs are the sources of ultra-high-energy cosmic rays (UHECRs). Methods. We simulate this scenario in a combined source-propagation model. While our key results are obtained using an internal shock model of the source, we discuss how the secondary emission from a GRB shell can be interpreted in terms of other astrophysical models. Results. We demonstrate that the expected neutrino flux from GRBs weakly depends on the injection composition for the same injection spectra and luminosities, 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 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.