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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). Within the internal shock model we choose parameters for the relativistic outflow such that our representative events have observed properties similar to GRBs 980425, 100316D and 120714B and self-consistently calculate the full spectral and temporal properties in a leptonic synchrotron self-Compton scenario. To investigate the conditions under which inverse Compton radiation may lead to a peak in the GeV--TeV range, we vary the fraction of internal energy supplying the magnetic field. Further, we determine the maximal energies achievable for UHECR nuclei and derive constraints on the baryonic loading/typical duration by comparing to the extragalactic gamma-ray background. We find that ll-GRBs are potential targets for multiwavelength studies and in reach for Imaging Atmospheric Cherenkov Telescopes (IACTs) and optical/UV instruments. For comparable sub-MeV emission and similar dynamical evolution of the outflow, weak (strong) magnetic fields induce high (low) fluxes in the VHE regime and low (high) fluxes in the optical. VHE emission may be suppressed by $γγ$-absorption close to the engine 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 (and the VHE component is correspondingly weak). These high energies are possible by decoupling the production regions of UHECR and gamma-rays in our multizone model. Finally, we find basic consistency with the energy budget needed to accommodate the UHECR origin from ll-GRBs.