Multicollision Internal Shock Lepto-hadronic Models for Energetic Gamma-Ray Bursts (GRBs)

For a subpopulation of energetic gamma-ray bursts (GRBs), a moderate baryonic loading may suffice to power ultra-high-energy cosmic rays (UHECRs). Motivated by this, we study the radiative signatures of cosmic-ray protons in the prompt phase of energetic GRBs. Our framework is the internal shock model with multicollision descriptions of the relativistic ejecta (with different emission regions along the jet), plus time-dependent calculations of photon and neutrino spectra. Our GRB prototypes are motivated by Fermi-Large Area Telescope-detected GRBs (including GRB 221009A) for which further, owing to the large energy flux, neutrino nonobservation of single events may pose a strong limit on the baryonic loading. We study the feedback of protons on electromagnetic spectra in synchrotron- and inverse Compton-dominated scenarios to identify the multiwavelength signatures, to constrain the maximally allowed baryonic loading, and to point out the differences between hadronic and inverse Compton signatures. We find that hadronic signatures appear as correlated flux increases in the optical-UV to soft X-ray and GeV-TeV gamma-ray ranges in the synchrotron scenarios, whereas they are difficult to identify in inverse Compton-dominated scenarios. We demonstrate that baryonic loadings around 10, which satisfy the UHECR energetic requirements, do not distort the predicted photon spectra in the Fermi Gamma-Ray Burst Monitor range and are consistent with constraints from neutrino data if the collision radii are large enough (i.e., the time variability is not too short). It therefore seems plausible that under the condition of large dissipation radii a population of energetic GRBs can be the origin of the UHECRs.