Multi-wavelength radiation models for low-luminosity GRBs, and the implications for UHECRs

We study the prompt phase of low-luminosity Gamma-Ray Bursts (LL-GRBs) as potential source of very-high-energy (VHE) gamma rays and ultra-high-energy cosmic rays (UHECRs). We model the spectral energy distribution of three representative events (with observed properties similar to GRBs 980425, 100316D and 120714B) self-consistently in a leptonic synchrotron self-Compton (SSC) scenario using the internal shock model for the relativistic outflow. To investigate the conditions under which inverse Compton radiation may lead to a peak in the GeV-TeV range potentially observable in Imaging Atmospheric Cherenkov Telescopes (IACTs), we vary the fraction of the internal energy supplying the magnetic field. Further, we determine the maximal energies achievable for UHECR nuclei and derive constraints on the baryonic loading and typical GRB duration by comparing to the extragalactic gamma-ray background. We find that LL-GRBs are potential targets for multi-wavelength studies and may be in reach of IACTs and optical/ UV instruments. For comparable sub-MeV emission and similar dynamical evolution of the outflow, the multi-wavelength predictions depend on the magnetic field: weak (strong) magnetic fields induce high (low) fluxes in the VHE regime and low (high) fluxes in the optical. VHE emission might be suppressed by $\gamma \gamma $-absorption close to the engine (especially for high magnetic fields) or interactions with the extragalactic background light for redshifts $z > 0.1$. For UHECRs, the maximal energies of iron nuclei (protons) can be as high as $\simeq 10^{11}$-GeV ($10^{10}$-GeV) if the magnetic energy density is large (where we found a weak VHE component). These high energies are possible by decoupling the production regions of UHECR and gamma-rays in our multi-zone model. Finally, we find basic consistency with the energy budget needed to accommodate the UHECR origin from LL-GRBs.